SR22T pilot reported the pilot entry door popped open during initial climb in rain and turbulence. Pilot returned to departure airport but turned wrong way from ATC clearance after landing and incurred on adjacent taxiway.

Narrative

I arrived at ZZZ around XA00 for an IFR flight plan flight from ZZZ to ZZZ1. Conditions upon arrival were poor; with convective activity; active hail; heavy rain; and wind gusts. I waited in the FBO for conditions to improve; and eventually around XB00; I started the engine to conduct the flight. Conditions were still poor; visibility was limited due to heavy rain and gusty winds persisted; but within my personal tolerance. Preflight checks were conducted with no issues noted; and I taxied to Runway XXR via 1. Tower cleared me for takeoff around XB30; and immediately after liftoff; I encountered severe windshear and moderate turbulence. I conducted the windshear escape procedure as taught in training. Upon reaching around 300ft AGL; the passenger side door popped open; and water began pouring into the cabin as well as loud wind noise. I informed the Tower of my situation and need to return; and they asked if I could maintain VFR and make left closed traffic. Radios were hard to hear; but I could decipher what was said and acknowledged; while also informing them I needed a wider than normal pattern due to the situation. I encountered severe mechanical turbulence at 600 ft AGL on the base leg coming over the hills; and low-level windshear +/- 15kt on final. Upon landing; strong wind gusts could be felt lifting the plane and I was continuing to have water leak onto me from the open door. Tower instructed me to exit the runway; but I do not recall which direction as the wind noise made the radios challenging to hear. I turned left on 2; which crosses XXL; and contacted Ground. I did not cross the hold short line of Runway XXL and contacted Ground; upon which the controller cleared me to cross XXL with 'no delay' and to copy a number for a possible pilot deviation. I stopped on a to close the door; then taxied to the 3 runup area to contact the Tower. I believe I turned left as is the standard procedure when landing to the south at ZZZ for FBO; and my expectation bias as well as adrenaline from the ongoing situation and challenging flying conditions as well as the ongoing problem led me to turn left instead of right as Tower had instructed.