EMB-145 Captain reported an air turn back after anti-ice systems failed after takeoff. After trouble shooting restored system operation; Captain reported Dispatch pressured him into continuing to destination airport with additional maintenance work.

Narrative

I was operating ZZZZ-ZZZ with a low time First Officer (FO). It was his second trip off of OE. Weather conditions in ZZZZ were IMC and conducive to icing. Runway XXR or XXL was in use. The ATIS noted there was 1/4 slush on both runways; we did not have the performance capabilities to depart either runway; and informed tower we required Runway XX. Visibility was 1/4 mile; so I was primarily eyes out on the takeoff. We were doing the ZZZZZ departure. At 400 feet; I called for 'NAV'. The FO pushed something else; I can't recall what. At this moment; we received a slew of messages on the EICAS. I hit NAV on the FGC (Flight Guidance Computer) myself; called for AP (Autopilot) and turned the AP on myself. I then looked over to process the messages- there were maybe 3-5. ICE COND/AICE INOP; maybe a low bleed; maybe ICE CONDITION; and definitely WG ANTI/ICE FAIL. I was quickly scanning for the root cause message- which to me was clearly WG ANTI/ICE FAIL. I reached over (as far as I could get on that panel); and immediately switched the override into the 'ALL' position. This did nothing. ATC attempted to give us a climb from 5;000 feet (the top altitude on the ZZZZZ) to 7;000 feet. We were in icing conditions. I told them unable; we were taking 5;000 feet; our wing-anti icing had failed and I am requesting priority handling. Tower gave us 5;000 feet and a right turn. Tower inquired about our intentions; and I informed them we would be running checklists and planned to come back around to land. Tower stated they would keep us in close to the airport. During the climb; I briefed the FO on the plan. Our gate fuel had been 7.4; and we needed to land 5.8 to not be overweight. I told him that we would accomplish the QRH once leveled off at a safe altitude. If the QRH did not resolve our issue; the plan was to get out of icing conditions immediately; and land immediately even if we were overweight. If the QRH did resolve the problem; I briefed that we would get completely set up; and land at max landing weight. At any point; we would try to exit icing conditions if possible. Ceilings were low. At this point; I didn't know if it would be possible to exit icing conditions while maintaining a safe altitude. Icing conditions and IMC existed in ZZZ1 and also along the route for the entire flight.Upon leveling off at 5;000 feet; I passed controls to the FO. I briefed him that I wanted him to fly whatever heading tower gave; and keep the airspeed at 200 knots since that's a safe; clean airspeed and because there's no use in going nowhere fast when we need to stay close. Tower told us to let them know when we were ready; and runway XX would be ours.I identified the QRH procedure we were following to the FO- 'Wing Anti-Icing Failure or Stabilizer Anti-Icing Failure'. The first item on the checklist is 'Ice Detector Override Knob- AUTO'; which I had already instinctively accomplished (and left in that position). Second is 'Thrust Levers- Advance'. Since this was accomplished during takeoff; I proceeded to: 'Message Persists?- Yes'. This directs you to 'Affected Ice Protection Button- Push Out; Then Push In.' Since I could not reach; I instructed the FO to accomplish this. The FO did as requested; and the system proceeded to function as normal. I briefed the FO that we would now take our time and do our due diligence in setting up; and hopefully our fuel would be burned off by that time. I paused the QRH to inform dispatch- the message I sent descriptive with all the important parts of our situation. Something in a more shorthand form; but along the lines of- 'Wing anti ice failed on takeoff. Performed QRH; which resolved issue. Plan on returning ZZZZ to land. Do you concur'. Dispatch messaged very quickly with 'I concur'. I noticed that ATC had vectored us quite well; and we were primarily out of clouds; it was just foggy/misty.I finished the QRH; electing to perform the set up for 'Landing In Icing Conditions Or With Ice Accretion'. I briefed the FO that this would be a flaps 22 landing per the QRH; set Vref to Vref 45+30 knots; based off of the 44;000 card. I used the QRH to multiply the flaps 45 unfactored landing distance by 1.85. Tower asked if we could land runway XYR rather than XX. I checked performance and accepted the runway. I then informed the FA of the situation and that we would be performing a normal landing; in about 10 minutes; definitely more rather than less. Her only question was if she needed to make a PA to the passengers. I told her I had a few things to do first; but I would make that announcement. I then circled back to our normals. After takeoff; cruise. I noted that we were timed perfectly to have enough fuel burned off to land just below max landing weight. I then made an announcement to the passengers- I stated the anti-icing system failure and the return to ZZZZ for a normal landing in about 10 minutes.I then set up for and briefed ILS XYR; and performed a general scan of the aircraft and set things appropriately for descent/landing. For the essence of time; I then read the checklists out loud to the FO while confirming appropriate positions. I took aircraft control back from the FO; and I accepted vectors from tower to the ILS XYR. At this point; tower had told me it was airport policy to roll the trucks so they had done so. I briefed the FO that we would now be stopping on the runway. Just after the FAF; I received an ACARS from dispatch; which stated (not verbatim)- 'if issue is resolved continue to ZZZ1'. Aside from being completely committed at this point; I feel that was an incredibly unsafe decision. Everywhere was IMC and icing conditions. I couldn't understand the reasoning behind their change of mind. (For reference; OOOI (Out; Off; On; In) times display there was 32 minutes from takeoff to landing. Dispatch had been initially notified 15-20 minutes prior to this. Here I was on short final; priority handling; fire trucks standing by; below my max fuel at landing of 5;803 pounds; and they truly suggested I carry on to ZZZ1 with 5;700 pounds or so of fuel on board. From the dispatch release: BO was 3.0; ALT 1.3; and RSV 1.6; the exact numbers from the release would require at least 5;877 lbs to do what they were requesting. I was flabbergasted. I performed a normal landing. Once stopped on the runway with the parking brake; I made the 'remain seated' PA to the passengers; but adding that they would see emergency vehicles which would inspect us; which is standard protocol for an emergency.We taxied into the gate with the trucks following us; per airport policy. At the gate; I made the phone calls to maintenance/dispatch. Dispatch stated via ACARS the reasoning to continue was because customs in ZZZZ had closed at XA:00 PM; and with their new hours; they wouldn't reopen until XM:00 AM. I was told to keep all passengers on the plane. I then spoke with Maintenance via the recorded phone line. Maintenance told me that Dispatch had forwarded my ACARS message to them; and asked why I hadn't continued to ZZZ1? Maintenance began questioning my decision making; basically telling me I handled the situation incorrectly. I guess maintenance had complete knowledge of the flight and did not agree that icing conditions along an entire route of flight were a threat to an aircraft that had just experienced an anti-icing system failure; since the system was back up again. Maintenance proceeded to tell me that what I experienced was a transient failure; since there was 'no history on the aircraft'. They further suggested I not write the aircraft up; and just continue on to ZZZ1. On the recorded phone line; I confirmed with them their awareness of what had happened; and that they did indeed want me to just do nothing about it; after requesting priority handling and performing an air turn back. They confirmed this was exactly what they were requesting; their multiple reasoning being; 'Contract Maintenance will take too longto come out there; there's no history on the aircraft; it was likely only a transient issue that doesn't need to be written up.' On the recorded phone line; I asked if they were asking me to risk my certificates. Maintenance then stopped suggesting that I specifically not write up the actual aircraft system that happened in a critical phase of flight; and check the Maintenance Controller. I said I did know where to find it; but I was so livid in that moment that I could not recall how to get there on the MFD. Maintenance instructed me; and I took a screenshot of the multiple failures and sent it to them via the text number. The maintenance messages were as follows: 'ENG1 Scheduled Maint Repair; WING1 A/ICE LOW PRESS; WING1A/ICE BURST; WING1 A/ICE VLV FAIL; PRECOOLER2 TEMP CTL SYS FAIL; DUCT TEMP SENSOR 1 FAIL;' I informed the passengers of the customs pickle by making a PA on the Flight Attendant's phone; coming through the cabin to answer those who had individual questions. My FA performed a service. The passengers eventually deplaned and were held in the gate area; unable to leave to get food/water. I do not know if they had access to any food/water during this time. I individually spoke with the FO and the FA to ensure they were good to continue on. We all decided we were. Contract maintenance met the aircraft fairly immediately after passengers disembarked. From what I saw; contract maintenance removed one small panel on the left wing root. I then performed multiple engine run ups with contract maintenance to test the system as they were instructed by our maintenance. The only test that were performed was our ice protection electrical test; as an FO would accomplish on origination during their flight deck scan. First it was done at idle thrust at the gate; which contract maintenance said it could be done at idle rather than the N2 required due to the temperature. This test failed. Then we taxied out; and did the test at 78% N2 on the aerodrome field. The ice protection test passed on the ground; and the aircraft was signed off. (Note: As far as weather conditions listed; it was IMC. I can't recall ceiling type; wind direction; or wind speed. Wind direction was somewhere in the realm of 30-40 degrees off the runway; around 10 knots or so. Ceilings were low likely broken; maybe overcast?)