ACR Y HAD LTSS FROM ACR X. SYS ERROR.

Narrative

ACR X ESTABLISHED ON THE 31R LOC. ACR Y ON BASE LEG VECTORS. I HAD TURNED ACR Y ON THE BASE LEG TO JOIN THE LOC IN FRONT OF ACR X; THEN REALIZED BOTH ACFT WERE AT THE SAME ALT. I ISSUED TURNS TO GET THEM APART. AT THE TIME I WAS WORKING BOTH THE DFW RWY 31R FINAL AND BOTH FINALS INTO DAL. AT DAL I HAD TO PULL 1 ACFT OUT AS THE ACFT WASN'T SLOWING QUICKLY ENOUGH AND CATCHING THE ACFT AHEAD. AT THE SAME TIME; AN ACFT AT DFW ON A MI FINAL COULD NOT COMPLETE HIS APCH DUE TO BEING TOO HIGH. I HAD TO PULL HIM OUT; ANOTHER ACR AT DAL STATED HE WASN'T GOING TO BE ABLE TO COMPLETE THE APCH; ANOTHER ACFT BEING VECTORED TO THE DAL FINAL WAS NEGATIVE XPONDER SO I WAS HAVING TO UPDATE THE TRACK CONSTANTLY; AND THEN ANOTHER ACFT HAD DEPARTED A SATELLITE ARPT (RBD) AND ENCOUNTERED IMC ON A VFR FLT PLAN. THERE WERE TSTMS IN THE AREA WITH SOME DEVS; ILS APCHS AT BOTH ARPTS; I WAS REALLY BUSY WITH EVERYTHING GOING ON. I ASKED FOR HELP (HDOF; OPENED ANOTHER FINAL POS FOR DAL) WHEN THE SIT OCCURRED. THE FINAL POS FOR DAL SHOULD HAVE BEEN OPEN. IF THIS HAD BEEN; THIS WOULD HAVE REDUCED MY WORKLOAD GREATLY; THE GARS; PULLOUTS MAY NOT HAVE OCCURRED; AND THE LOSS OF SEPARATION PROBABLY NEVER WOULD HAVE HAPPENED.