AN ACR MLG BADLY EXECUTED A GAR. THERE WAS AN ALTDEV; A HDG DEV; AND A TCASII ALERT.

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UPON REACHING THE DH ON THE ILS 31R APCH AT DFW; I DECIDED TO DO A MISSED APCH. DURING THE GAR; THE FO CALLED FOR 'FLAP 15' AND 'POSITIVE RATE GEAR UP.' UPON PLACING THE GEAR HANDLE TO UP; THE VERBAL LNDG GEAR WARNING SOUNDED WHILE THE FLAPS WERE STILL IN THE LNDG RANGE. THIS CAUSED SLIGHT CONFUSION. A CALL WAS THEN MADE TO THE TWR THAT WE WERE GOING AROUND; BUT; DUE TO FREQ CONGESTION THE XMISSION WAS BLOCKED; SO; I TRIED AGAIN BUT NO RESPONSE. THE ACFT WAS ACCELERATING VERY RAPIDLY TOWARD 250 KTS; AND THE AUTOTHROTTLES WERE STILL IN GAR MODE. I THEN ORDERED THE FO TO GO TO 'SPD SELECT' WHILE MOVING THE SPD SELECT BUG TO CLEAN MIN MANEUVERING SPD. I REMINDED HIM TO START A R TURN DIRECT TO 'BLUE RIDGE' VOR. THEN WE RECEIVED A 'TA' FROM THE TCASII SYS FOLLOWED IMMEDIATELY BY A CLB 'RA;' I COMMANDED THE FO TO FOLLOW THE 'RA;' THE ENTIRE TIME; 'CLB; CLB; CLB;' AURAL WARNING SOUNDING. DURING THE LATER PART OF THE 'RA;' THE ACFT PASSED THROUGH THE ALT SET IN THE ALT ALERT WINDOW. THE VERBAL ALT WARNING STARTED SOUNDING CONTINUOUSLY; ALONG WITH THE TWR ISSUING A HDG OF 280 DEG FOR US TO FLY. I THEN READ BACK HDG 280 DEG AND THE TWR SAID NEGATIVE; FLY HDG 360 DEG. NOTING THE AIRSPD WAS DECELERATING RAPIDLY (DUE TO 'RA' CLB COMMANDS); I TOLD THE FO TO REDUCE PITCH ATTITUDE. AFTER THIS POINT; WE REESTABLISHED OUR HDG AND ALT AS DIRECTED BY THE TWR; AND CONTACTED DEP CTL. I CONSIDERED TAKING CTL OF THE ACFT AWAY FROM THE FO; BUT OPTED NOT TO DO SO BECAUSE; I FELT A CHANGE OF CTL DURING THIS CRITICAL PHASE OF FLT MIGHT FURTHER COMPROMISE THE SAFETY OF OUR FLT. IT IS MY OPINION THAT DURING A CRITICAL PHASE OF FLT THE VERBAL WARNINGS HINDER OUR ABILITY TO CONCENTRATE AND MISS THEIR PRIME OBJECTIVE TO CORRECT THE ASSOCIATED PROBLEM. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. THE RPTING CAPT STATES THAT HE PROBABLY SHOULD HAVE BEEN MAKING THE APCH; BUT THE RPTED WX WAS 300 FT AND 1/2 MI VISIBILITY. THE ACFT WAS STILL IN THE CLOUDS BELOW 200 FT. THE RPTR DID GET A GLIMPSE OF THE APCH LIGHTS UPON ROTATION. THE TCASII WAS LEFT IN TA/RA WHEN IT SHOULD HAVE BEEN PUT IN TA ONLY. THE ACFT DIVERTED TO LOVE FIELD WHERE THE CREW WENT 'ILLEGAL'. THE FO APOLOGIZED FOR HIS ACTIONS. THE CAPT HAS NOT HEARD FROM THE FAA OR HIS COMPANY. TO MAKE MATTERS COMPLETE; THERE WERE TSTMS AND WINDSHEAR IN THE AREA. DFW RWY 31R IS A CAT I APCH WITH WX MINS OF 200/ 1/2.