C182 PILOT LOSES CONTROL IN IMC WHEN ATTEMPTING TO ENTER WRONG VOR IDENTIFIER IN GPS.

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WORKING WITH ZAU WHILE IN IMC; I WAS PROCEEDING DIRECT TO BRADFORD VOR (BDF) FROM THE MAPPS INTXN WHEN I WAS GIVEN A NEW CLRNC TO PROCEED DIRECT TO MY DEST WASHINGTON MUNICIPAL (AWG). I WAS ATTEMPTING TO ENTER THAT NEW WAYPOINT INTO THE GPS (APOLLO GX50; IFR CERTIFIED) AND WAS HAVING DIFFICULTY GETTING THE GPS TO ACCEPT AWG. BEING DISTR FOR THOSE FEW SECONDS (ESTIMATE ABOUT 8 SECONDS); I ENTERED AN UNUSUAL ATTITUDE OF ABOUT 50 DEGS R BANK. WHILE TRYING TO RECOVER TO LEVEL FLT; I GOT OFF COURSE ABOUT 120 DEGS TO THE R AND LOST ABOUT 500 FT ALT. WHEN I DID ACHIEVE LEVEL FLT; I WAS DISORIENTED ENOUGH SO THAT I DIDN'T IMMEDIATELY CORRECT MY HDG TO THE GENERAL DIRECTION I KNEW MY DEST WAS BEFORE I RECEIVED A CALL FROM CTR ASKING ME TO STATE MY HDG. SINCE I WASN'T CERTAIN WHAT MY HDG WAS YET; I REQUESTED AN INITIAL HDG TO TURN TO AND WAS TOLD TO TURN L TO A HDG OF 240 DEGS WHICH I WAS ABLE TO ACCOMPLISH. NO FURTHER ASSISTANCE WAS REQUESTED NOR WAS IT REQUIRED AS I HAD DETERMINED ABOUT 1/2 MIN LATER MY PROB WAS CAUSED BY TRYING TO ENTER AGW INSTEAD OF AWG. UPON ENTERING THE CORRECT WAYPOINT; I DETERMINED A FURTHER HDG CORRECTION TO 270 DEGS WAS REQUIRED. WITH THE CORRECT HDG; I PROCEEDED TO MY DEST WITH NO FURTHER PROB. I WAS WELL WITHIN THE WT AND BAL REQUIREMENTS BEING AT 2812 LBS (138 LBS UNDER GROSS) AND 118 INCH/LBS (/1000) MOMENT. CONTRIBUTING FACTORS: THE AIRPLANE WAS FLYING WITH THE R WING HVY WITH NEARLY FULL FUEL TANKS AND A HVY PAX IN THE R SEAT AND SOME HVY CARGO LOADED ON THE R SIDE OF THE BAGGAGE COMPARTMENT. AT THE TIME OF UPSET I WAS IN SOLID IMC WITH MODERATE TURB. SINGLE PLT WITH NO AUTOPLT IN IMC MOMENTARILY DISTR BY DIFFICULTY OF ENTERING NEW DATA INTO THE GPS.