EMB-190 Captain reported severe weather and turbulence resulted in the failure of #2 engine. The flight crew elected to divert.

Narrative

Upon our descent to ZZZZ we were cleared to point ZZZZZ; established at FL350; and approaching ZZZZZ we were put on radar vectors due heading 290 for preceding traffic. At this time we noticed that this heading was sending us into the direction of convective cell; direct and slightly to the right of that heading. With our radar parked for our current altitude; we could tell the cell had a sharp green/yellow/red radar return. And it appeared to be at approximately 20 miles and slightly off the nose of the aircraft. The estimated cell diameter was 10-20 miles. In instrument conditions at the time; we were unable to acquire the cell visually. At a certain time on this heading; we were additionally given a descent. Concerned for our course toward the convective cell; we queried the controller; and advised we needed a turn. He answered our request with I will turn you in 1 minute; from what I remember. We had a certain amount of trust the controller would turn us prior; and I wondered at the time if the controller could see the same weather that we were seeing on our radar. And his responses seemed to match a shared concern. A false sense of ATC security I think was assumed by the crew. After a certain amount of time the controller gave a present position direct to a point that was unfamiliar and hard to understand. We queried the controller about that point; and under confusion possibly; he gave us a heading of 310 which placed us into a more direct vector into the cell; which was unhelpful; and time was running out. Maybe the heading was issued to ensure separation of that traffic to the left; the traffic at approximately 1;500 ft. below and to the left; skirting the storm. At this point; I should have exercised a deviation as required and let the TCAS do its job if there were any additional traffic in the area. Not having the full picture; and deviating in the presence of traffic was a concerning factor.In IMC at the time; we knew we had minimal time to deviate; we penetrated the storm; shortly into the penetration; I kicked the Autopilot off and tried a steeper turn to the left to possibly avoid further penetration of the storm. It was too late and the severe turbulence and hail ensued immediately. I struggled with aircraft control and trying to maintain a reasonable speed in the event. At certain points seeing -3;000 ft. vertical speed indicator (VSI) and high speed warnings. I have never experienced such a violent flying experience. The hail was so loud inside the aircraft; the First Officer (FO) was trying to report the #2 Engine Fail EICAS message; I could not hear him; and didn't realize the engine failure until I noticed the split throttles and auto throttles disconnected. At that time he was still attempting to communicate the failure. This all happened very quickly. I directed the FO to accomplish the checklist; while I focused on the HUD and maintained aircraft control wings level. The initial Engine Fail is a QRH item. Following the procedure determined engine 2 had a windmilling N1; but with an extremely high Interstate Turbine Temperature (ITT); approximately 1111 degrees; and a notable mechanical vibration. We were redirected to the QRC for the engine shutdown via the Engine 1(2) Fire/Severe Damage/Separation (In Flight) QRC. Aircraft control was difficult; and during the situation; I had to rely on and trust the FO's Non-Normal procedure ability; and I had to focus on flying the aircraft. The FO did a noteworthy job analyzing the aircraft malfunctions and checklist discipline. After coordinating the shutting down of the #2 Engine we followed up with the additional EICAS messages needing addressed. Other EICAS messages were A-I Wing Fail; Ice Detector 1 Fail; AFCS Fault; LANDING LT RH Remote CB trip; and Bleed 1 Fail/Off. These are the messages; that I know of; once we got on the ground; others could have been annunciated during flight; but can't recall exactly every message. Eventually we exited the storm; mind you all this was occurring at the same time. While handling the aircraft; ATC was issuing altitudes and asking distracting untimely questions. I remember them wanting us to descend to FL200. Exiting the storm single engine; Engine #1 still operational; as far as I could tell; I was concerned with its condition and performance. And initially told the FO we could take intermediate level off of FL250; then shortly said we could take FL200; since lower would be better for southeast performance and the bleed 1 being offline. No bleeds were available at this time; and I was concerned to restart the bleed 1 and introduce any stress to our last remaining engine that may have had damage. So our best course of action was to descend; but on our terms to ensure terrain clearance. My confidence with control at this point was minimal. Once good communication was established; [priority handling requested]; and out of the event; ATC suggested an airport closer to our current location; but at our altitude and position; ZZZZ was our best nearest suitable airport per the QRH. This would afford us time; terrain deconfliction; and limited airfield familiarity; we had discussed terrain and descent strategies enroute and the high MSAs. Exiting the storm we were in VMC; and only had light weather; small puffy clouds on our turn back to ZZZZ; but weather was still concerning. *A noteworthy occurrence; during this event and flying toward ZZZZ; a new controller; possibly a supervisor; stepped in; for whom spoke very clear English; and gave us clearances and vectors; then shortly the previous controller took back over.During our flight from the event to the ZZZZ; we got a clearance at certain time to 13;000 ft.; and we were still very busy handling the aircraft system malfunctions and getting ready for the approach and determining our Non-Normal landing data; and completing normal checklists and procedures. Approaching the field and descending the controller gave us approach clearance for the VOR approach; he did not specify which runway; which I thought was an ATC requirement; so we had to clarify VOR DME 1 Runway XX; full procedure; teardrop. He also gave us the option for the visual to Runway XX also; not doing a short turn to final in quite some time in the E190; it didn't seem like a good time to practice now; and at this time the remaining engine appeared to be operating normally. I focused on maintaining a good energy state. Approaching ZZZZ from the northwest; at approximately 7 miles we were VFR and getting below the cloud obscuration.Backing up; during our event exit and proceeding to the field we had no pressurization due to the Engine #2 shutdown and Bleed 1 Fail/Off; so the cabin was slowly rising; but my concern was turning the bleed back on with the QRH and introducing any stress on the remaining engine. So our focus was descending the aircraft and ensuring terrain clearance. The 13;000 ft. ATC clearance worked for us so we focused on getting to that altitude; and we knew the approach procedure started at 10;000 ft. and we would be at that safe altitude in short time. Intimately knowledgeable with aviation physiology; I knew we were safe at or below 14;000 ft. without supplemental oxygen; and a good trigger would be if the cabin oxygen masks deployed; we would definitely go on supplemental oxygen per the memory items. I did not verbalize this with the FO; and will accept pilot in command (PIC) deviation authority and responsibility on this. I was concerned that the communication barrier with the masks may be too much of a barrier for us accomplishing requirements. And this was not a rapid decompression or a high cabin altitude situation. We did hear the Cabin High annunciation. We leveled at 13;000 ft. going direct to ZZZ VOR and at that point we were still VMC and almost below some obscuration between us and the approach to the field. We allowed the aircraft to VNAV descend on the teardrop and focused on ensuring that all checklistswere complete and communicating any anomalies and questions that we may have. I was really concerned if we had to go around on the approach with high field elevation and terrain; and one engine that could be possibly damaged. The approach and landing was uneventful. Upon landing we rolled to a stop on Taxiway X allowed the Crash Fire Rescue (CFR) to survey the #2 engine and entire aircraft; and they relayed through Tower everything appeared secure. We could see the marshaller for the depot maintenance facility on the ramp from our position on X and said we could probably taxi there. But after a quick reconsideration and discussion; we decided to shut down the aircraft on X and allow Maintenance to tow us to the ramp with aircraft APU power. During our CFR observation; we were ready with evacuation checklist; in the event evacuation was required. Once in parking we shutdown the aircraft per the checklist; and disarmed the doors. I talked to Maintenance and made the required logbook entries. I verbally handed the aircraft over to Maintenance with the APU running.Notable events handled on the flight: Controller vectors (lack thereof); Controller proficiency; High altitude maneuvering; Unusual attitudes; Severe turbulence; Severe precipitation; Engine failure; severe damage (high ITT); High Cabin Altitude; Aircraft Structural limitations; Cabin Altitude HI; High terrain; High field elevation; Full procedure approaches with multiple aircraft malfunctions; Fuel imbalance