AN ACR MLG AND AN SMT HAD LTSS IN THE WX. TCASII AND TRACON WERE GIVING BOTH COMPLEMENTARY AND CONFLICTING INSTRUCTIONS BEYOND THE CAPABILITIES OF THE ACR ACFT.

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FLT DEPARTED VPS RWY 12. AT 2000 FT CLRED TO 10000 FT; L TURN TO 090 DEGS. IN THE TURN; FURTHER CLRNC TO 030 DEGS. AT ABOUT 4000 FT IN THE TURN; TFC APPEARED AT 10 O'CLOCK ON TCASII. STILL IN THE TURN; FURTHER CLRNC TO 360 DEGS. (FLT NOW IN IMC; INTERMITTENT VISIBILITY UP TO NO MORE THAN 1/4 BTWN BUILDUPS.) BEFORE ROLLING OUT ON 360 DEGS; ADVISED OF TFC 'EBOUND SMT; 10 O'CLOCK; 5000 FT.' TCASII WENT INTO RA MODE 'DSND; DSND' THEN ATC ASSIGNED 330 DEGS; FOLLOWED BY A REQUEST TO TIGHTEN THE TURN (EXACT WORDING NOT RECALLED); FURTHER L TO 290 DEGS. BY THIS TIME; I HAD REVERSED MY CLB AT ABOUT 4800 FT. TCASII NOW GETTING EXCITED; 'INCREASE RATE OF DSCNT.' TFC SYMBOL ON TCASII PASSED OFF OUR R SIDE (ABOUT 2 SYMBOL WIDTHS ON THE TCASII) AS WE WENT THROUGH 4500 FT. TCASII 'CLR OF CONFLICT.' CONTINUED TURN TO 290 DEGS; REVERSED DIVE; CONTINUED CLB TO ASSIGNED ALT. REST OF FLT UNEVENTFUL. NO COMMENT FROM ATC. I ALSO BELIEVE THE SMT WAS NOT AWARE OF OUR PRESENCE. NO VISUAL CONTACT EVER MADE. I FELT AT THE TIME THAT DEP CTL WAS TRYING TO TURN ME INSIDE THE TFC. AT 220 KIAS AND 30 DEGS BANK A HVY MLG IS PONDEROUS AT BEST; CANNOT CLB QUICKLY NOR IS IT CHANGING HDG VERY QUICKLY.