Air carrier flight crew flying an ERJ-170 aircraft reported autopilot and pitch trim failure inflight.

Narrative

I was PM (Pilot Monitoring) on Aircraft X to ZZZ while the FO (First Officer) was PF (Pilot Flying). During a continuous descent from higher altitude; passing around I believe FL200 down to FL190; when we felt three or four partial rolls; almost like wake. The AP was kicked off; right about the time we received a clearance to descend to 11000 and 250 at ZZZZZ. We told ATC we would not be able to make the restriction; and would need some vectors and a delayed descent to work through the QRH procedures. The AP Fail and Pitch trim fail cautions were displayed; I opted to start with the pitch message; however; was interrupted several times with questions or requests to do a hold when we had asked for vectors so we could complete QRH procedures. After ATC eventually gave us discretion with doing a slow 360 back to the airport; We initiated the pitch trim malfunction procedure; finding that the message came back nearly immediately after the trim cut out switches were cycled; we concluded that checklist with the abnormal procedure which required us to cut off the pitch trim; [advise ATC] and land. We determined our best course was to continue to ZZZ as it was close; and would afford time to work through the trim malfunction descent and Landing checklists; as well as communication with Dispatch; FAs (Flight Attendants); and passengers. We [advised ATC]; I followed with the AP fail checklist; and then moved to the descent checklist. Once the runway setup was completed; landing distance calculated; and landing speeds entered; I relieved the FO of flying as she had been flying without trim for some time now; and opted to have her finish the flight as PM (Pilot Monitoring) where she contacted Dispatch; kept the passengers informed; and worked the radios and checklists until landing. The remainder of the flight consisted of setting up for a long final; configuring to different speeds early to assess the controllability of the aircraft without pitch trim and landing at ZZZ without further issues. We taxied to the gate without further incident; contacted Dispatch; and then contacted Maintenance.Several interruptions by ATC initially when we told them we needed to stop descent and might need delay vectors to run QRH procedures delayed me several times; just trying to index the first procedure and was interrupting communication between the FO and myself. Additional problems were added to our list when rather than giving vectors as we asked; ATC gave us a present position hold; which initially I had selected in the FMS; and then as I was entering the direction of turn; the FMS suddenly cleared the hold and refused to allow present position holds to be placed in the flight plan. We spent several minutes trying to setup holds rather than dealing with the QRH before we ultimately told ATC we were unable. If ATC has been told that an aircraft needs time for procedures; there needs to be some awareness that asking a new question every 10-20 seconds only prolongs the problem.