MCI CTLR EXPERIENCED OPERROR ATTEMPTING TO VECTOR ONE ACFT BEHIND ANOTHER AT 4000; CITING WINDS ALOFT AS A FACTOR IN THE EVENT.

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I WAS WORKING DEP RADAR (E AND W COMBINED). ADDITIONAL POS OPEN WERE SATELLITE (N AND S COMBINED) AND ARR (WITH FINAL COMBINED TO IT). THE WIND WAS STRONG OUT OF THE E; PUTTING US ON AN E FLOW -- NONSTANDARD FOR OUR FACILITY. THE P32R WAS A DEP FROM MCI WBOUND TO SLN (FILED FOR 6000 FT BUT LATER REQUESTED A CHANGE TO 4000 FT) AND THE PA32 WAS A DEP FROM OJC (AN ARPT S OF MCI) SLATED TO EXIT THE AIRSPACE THROUGH OUR NW DEP GATE AT 8000 FT. THE INVESTIGATION SHOWED I HAD 11 AIRPLANES AT THE TIME. XA11: P32R DEPARTED MCI AND CHKED ON LEAVING 1800 FT FOR 4000 FT ON A 140 DEG HDG (OUR STANDARD PROP DEP ALT AND HDG FOR E FLOW) -- PA32 CHKED ON AT 3000 FT ON A 330 DEG HDG (HDOF FROM SATELLITE). I CLBED THE PA32 TO 6000 FT FIRST; THEN I ACKNOWLEDGED THE P32R AND REAFFIRMED 4000 FT. I TURNED THE P32R S TO AVOID MKC AIRSPACE. XA13: I ISSUED THE PA32 A 360 DEG HDG (VECTOR AROUND MCI ARR AIRSPACE AND DEP CORRIDOR). I ISSUED THE P32R A 220 DEG HDG THINKING THE WIND WOULD PUSH HIM FURTHER W; XING THE FLT PATH OF THE PA32; BUT STILL AVOIDING ARR AIRSPACE TO THE W (TRAINING IN PROGRESS ON A BUSY ARR SESSION). XA16: I NOTICED THE 2 ACFT GETTING CLOSE AND THAT THE PA32 WAS ONLY CLBING OUT OF 4200 FT. I TURNED THE P32R R TO A 300 DEG HDG. COLLISION ALERT ALARMED DURING PLT'S READBACK. I TURNED THE PA32 R TO A 090 DEG HDG. TFC WAS EXCHANGED; BOTH ACFT REPLIED WITH 'LOOKING' (IT WAS HAZY). MY INTENT WAS TO PUT THE ACFT ON XING COURSES INSTEAD OF CONVERGING COURSES; SO THE P32R WOULD BE W OF THE PA32. MY HDGS (220 DEGS AND 360 DEGS) WERE CONSERVATIVE; SO I COULD SEE THE EFFECTS OF THE WIND AND ADJUST AS NECESSARY. I WAS TRYING TO AVOID ARR AIRSPACE AND THE MCI DEP CORRIDOR. I ALSO THOUGHT THE PA32 WOULD CLB ABOVE THE P32R. THE P32R HAD TO CLB 2200 FT TO REACH 4000 FT WHILE THE PA32 HAD TO CLB 2000 FT TO REACH 5000 FT (1000 FT SEPARATION). OVER 4 MINS PASSED FROM THE TIME I ISSUED THE PA32 A CLB (3000 FT TO 6000 FT) TO WHEN I NOTICED THE ERROR. I HAD PLANNED TO MONITOR THE SITUATION AND ADJUST AS NECESSARY; BUT I GOT BUSY WITH OTHER TFC AND COORD; AND DIDN'T GET BACK TO THIS SITUATION IN TIME. ALL 3 POS WERE WORKING BUSY TFC IN A RARELY USED/DIFFICULT FLOW FOR LONG PERIODS OF TIME (I WAS PREVIOUSLY ON SATELLITE FOR 2 HRS 19 MINS). SATELLITE TOLD THE SUPVR THEY NEEDED HELP; SO THE SUPVR'S ATTN WENT TO ASSISTING THAT POS. WE DIDN'T HAVE ENOUGH PEOPLE TO SPLIT OUT POS WHEN NECESSARY; SO I BELIEVE STAFFING WAS A CONTRIBUTING FACTOR.