A11 Controller providing OJT; described a minimal separation event; indicating they should have taken control of the position earlier.

Narrative

I was working Aircraft X who went around initially the reason was unknown. I attempted to vector him back in for a visual approach. He said he had the aircraft lights but said the aircraft was below a layer. I vectored Aircraft X across the localizer to re sequence and assigned 020 feet and heading 270. Aircraft Y was on vectors to intercept the localizer and initially cleared for the approach; I noticed Aircraft Y at 028 feet; when I realized I would not have the required separation; I went back to Aircraft Y and issued 'maintain 030 feet fly heading 090'; Aircraft Y read back 'verify maintain 030 feet' and I said 'affirmative maintain 030 feet affirmative 030 feet' he stated 'heading 090 maintain 030 feet. I noticed Aircraft Y at 028 feet; the altitude never changed to 030; I assumed his altitude may have been off by 002 feet. I cleared him for approach and he landed without incident. Aircraft X was vectored back to the ILS approach and landed without incident. Recommendation; playing Monday morning quarterback; I would have taken over the position from the trainee when I noticed he was getting behind earlier than what I did. I would have had the trainee sequence allot farther back and been in a position to make a better flow to the airport. I allowed the trainee to set up a situation that I saw as a problem; while we were discussing how to better feed our self we had the go-around with Aircraft X. I should have inquired better with the Tower as to why Aircraft X went around; which would have told me to not try and get him back in on a visual; they had been working fine up to that point. As for the reason for the report; while I feel the separation was adequate; the fact that Aircraft Y remained at 028 -vs- 030 even after he verified 030 caused me concern as many people were closely watching and listening; and I felt I could have done better with Aircraft X. The pilot in charge of Aircraft X flight did call the facility to tell me I did a great job with the conditions we had. I just wished I could have done it differently.