A DEHAVILLAND -8 MADE A MISSED APCH AND DIVERTED DUE TO TSTM ACTIVITY AND WINDSHEAR. A FAILED WX RADAR WAS DECIDING FACTOR TO DIVERT.

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WE DEPARTED ZZZ1 ENRTE TO ZZZ WITH 4000 LBS OF FUEL ABOARD AT XA46 EDT. OPS WERE NORMAL UNTIL JUST S OF ZZZ2. WE WERE HANDED OFF TO ZZZ APCH CTL. WE ASKED FOR RWY 17 DUE TO THE S WINDS AND SHORTER DISTANCE. ATC ADVISED THAT THERE WERE LEVEL 4 TSTMS ON THE ILS RWY 17 FINAL; ALTHOUGH OUR WX RADAR DID NOT INDICATE ANY SIGNIFICANT RETURNS. ATC RECOMMENDED ILS RWY 26; AND WE ACCEPTED. ATC STATED THEY WERE VECTORING US BTWN 2 CELLS; AND WE TOLD THEM THAT THEIR RADAR WAS BETTER THAN OURS; SO THEY SHOULD CONTINUE. THE RVR ON RWY 26 WENT BELOW MINIMUMS BEFORE THE FAF; SO WE ACCEPTED VECTORS TO RWY 27R AT ZZZ. AFTER THE FAF ON RWY 27R; WE ENCOUNTERED A SIGNIFICANT WINDSHEAR OF -40 KTS AND INITIATED A MISSED APCH. AS WE MISSED THE APCH; THE LNDG GEAR DOORS DID NOT CLOSE PROPERLY. WE ENCOUNTERED SIGNIFICANT TURB ON THE TURN TO THE SE AND SO CONTINUED THE TURN TO A 090 DEG HDG. WE THEN ENCOUNTERED AN UPDRAFT THAT PRECLUDED ME FROM LEVELING OFF AT 2000 FT MSL. ATC APPROVED 3000 FT MSL AND THE 090 DEG HDG. WE BELIEVED THAT OUR 'OUT' WAS TO THE E. WE FELT THAT ZZZ3; OUR PUBLISHED ALTERNATE ARPT; WAS BEYOND REACH DUE TO THE WX AND DID NOT WANT TO FLY N DUE TO THE KNOWN LEVEL 4 CELLS THERE AND DID NOT WANT TO GO S DUE TO THE SIGNIFICANT TURB. WE CHKED THE ZZZ4 WX; AND IT WAS ACCEPTABLE. WE ADVISED ZZZ OPS OF OUR DECISION TO PROCEED TO ZZZ4 AND ASKED THAT THEY ADVISE DISPATCH. THEY DID SO. WE RESOLVED THE LNDG GEAR PROB USING THE EMER CHKLIST; AND SPOKE TO THE FLT ATTENDANT AND THE PAX. WE MONITORED XXX. XXX ON THE #2 RADIO AND DID NOT RECEIVE ANY CALLS. UPON ARR AT ZZZ4; ATC SLIPPED US BTWN ARRS; AND WE FLEW A 10 MI FINAL UTILIZING THE ILS RWY 22. WE LANDED WITH 2300 LBS OF FUEL AT XC33 EDT. WE WROTE UP THE WX RADAR AS BEING MARGINAL AND WROTE UP THE LNDG GEAR FOR NOT RETRACTING PROPERLY.