FAILED GYRO SLAVING UNIT RESULTS IN TRACK DEVIATIONS AND LOSS OF SEPARATION FOR IFR BE58 PLT.

Narrative

UPON DEP FROM RWY 16R AT ZZZ; I ENTERED IMC FLYING BY MY PRIMARY FLT INSTS (6-PACK). UPON ENTERING IMC; I BEGAN TO RECEIVE CONFLICTING DIRECTIONAL INFO BTWN MY HSI AND GPS. I DETERMINED THAT MY ATTITUDE INDICATOR WAS GIVING CORRECT INFO AND HELD WINGS LEVEL UNTIL CLRING IMC AND REACHING VFR ON TOP. DURING THIS TIME I WAS QUERIED BY ATC REGARDING MY HDG. I ADVISED I WAS HAVING AN ISSUE WITH MY NAV EQUIP. WHEN I ENTERED VFR; I REQUESTED ASSISTANCE IN THE FORM OF A HDG AND ALT SO I COULD ATTEMPT TO IDENT AND RECTIFY THE PROB. I WAS ADVISED BY ATC TO RETURN TO ZZZ. I DECLINED THIS REQUEST AS PIC AND ADVISED ATC THAT IT WAS NOT SAFE DUE TO FAULTY AND/OR CONFLICTING NAV INFO BEING RECEIVED. A RETURN TO ZZZ WOULD HAVE MANDATED AN INST APCH PROC BACK THROUGH IMC; AN APCH THAT I DETERMINED TO BE UNSAFE AND LIFE THREATENING. UPON REACHING THE ASSIGNED ALT AND HDG; I ATTEMPTED TO TROUBLESHOOT THE PROB AND DETERMINED THAT THE SLAVING UNIT FOR THE HSI HAD BECOME INOP AND THAT THE HSI HAD PRECESSED SIGNIFICANTLY SHORTLY AFTER GEAR RETRACTION AND UPON ENTERING IMC; CAUSING THE DEV FROM MY ASSIGNED COURSE. AFTER MANUALLY SLAVING THE HSI AND DETERMINING THAT THE HSI WAS REFLECTING CORRECT NAV INFO WITH THE AUTOMATIC SLAVING UNIT TURNED OFF; I ADVISED ATC THAT I HAD RESOLVED THE ISSUE AND REQUESTED TO CONTINUE TO MY DEST; WHICH I KNEW WAS EXPERIENCING VFR WX. ATC ADVISED THAT I HAD LOST SEPARATION WITH ANOTHER IFR ACFT DURING THIS INCIDENT AND ADVISED ME TO CONTACT FSS.