BE-58 Captain reported becoming disoriented during IMC weather and turbulence while under ATC control resulting in altitude and heading deviations. The pilot regained aircraft control; climbed above the turbulence and continued the flight.

Narrative

I was practicing IFR approaches in actual IMC between 2 adjacent (XXnm) airports (ZZZ and ZZZ1). As i approached ZZZ1 ATC kept adjusting my vectors to final due to significantly higher winds aloft than expected. At one point i reported my aspen EFD was indicating a 42kt wind; which was met with a 'wow' from ATC. Upon going missed at ZZZ1 (as planned); i signed off from CTAF; began turning the controls for a climb to 2;000msl; entered IMC; and turning to 220; as previously instructed by ATC. I reported back to Center; while also reducing power to stop by climb at 2;000 msl. ATC immediately began vectoring me around traffic; with a stern reminder to stay at or below 2k; i observed 2;175 indicated altitude; so pushed down on the yolk; but with the reduced power and turbulence; I immediately descended to ~1;800 indicated. To correct this I pulled up slightly; but hadn't notices that i was in a sharp turn to the right; which was also resulting in a sudden loss of altitude. ATC call to alert me that they had me at 1;500 msl and ask 'are you ok'; i responded yes; it's just very bumpy. I looked at the EFD and observed a sharp turn to the right and slight nose down indication. To correct; I leveled the controls to stop the turn; pulled up to stop the decent and began to climb back to 2k feet. ATC turned me to 270 and instructed a climb to 4k to get above the weather. the rest of the flight was normal; with vectors to final on the RNAV XX at my destination airport ZZZ. Cause: I had likely become disoriented when inadvertently make a hard right turn and descending to 1;500ft; i'm assuming the turbulence and high winds blew me sideways and with a high level of task saturation; i did't notice until ATC alerted me. Solution: While practice in IMC might be a great way to stay proficient; i should have continued using the autopilot upon going missed to help reduce the workload for maintaining heading and altitude. I wanted to manually fly the climb out; but in hindsight that was not the best decision. Maybe just using the Aspen Flight Director is a good compromise between manually flying and using the autopilot (AP).