AUS Controller described a near separation loss event when required in trail distance was minimal and visual separation was necessary; the reporter noting the need to curtail some ATC action when traffic dictates.

Narrative

I had several arrivals and was doing ILS approaches to Runway 17L/17R. I had an EA45 doing practice approaches. The pilot was a student and I had difficulty with them on every approach. They were on a right downwind to Runway 17R and I turned them to a heading of 010 to get closer to the turn on point. The pilot was a student and they turned to a 100 or 110 heading; well inside the turn on point. When I realized they had turned too far; I climbed them and turned them southbound. I believe this was a pilot deviation; although I do not recall the read back of the assigned heading. I had numerous other arrivals and this messed up my sequence and threw me off. It put them in a bad place on final and my mind was trying to figure out where to re-sequence them. I had altitude with everyone; but there were more arrivals still coming. I sequenced a few more aircraft and had a BE35 for 17L behind; I think; a regional jet. I kept altitude as long as I could and then finally cleared the Bonanza for the ILS approach anticipating that he would slow down and my 3+ miles would become 4 miles. Although I kept slowing the Bonanza down; the space between them did not spread out as much as I had anticipated. When the RJ was at the threshold it did not appear to be quite four miles so I asked the Supervisor if I should break the Bonanza out and he/she said yes. I issued climb instructions and tried to turn him but; he said he had the airport in sight. I cleared him for a visual approach and then at the prompting of the Supervisor made sure he also had the RJ in sight and told him to maintain visual separation. Partially; I was hesitant to send him around because I had planes stacking up and the EA45 was also out there that I had to re-sequence. I think once the EA45 proved difficult; I should have ended his approaches and sent him on his way. I'm not sure what the separation was with the Bonanza and the jet on final. Recommendation: 1. End practice approaches to aircraft when it becomes busy; especially student pilots who are having a difficult time. 2. Don't hesitate to break out aircraft on final with overtake; even if it is 'just' a Bonanza. 3. Don't take hand offs from feeders until I have somewhere to put more arrivals.