Getting into a PGY 2 position is not an easy thing. Very few programs have them, and when they are available, the program often times gives them to candidates without announcing it to the public. As a former program director of mine put it, if he were to just ask everyone in the department if they knew anyone wanting a PGY-2 position, he'd get about 15 good people. If he put it out to the public, he and the program coordinator would be inundated with applications, and the PC would get annoying phone calls from several people begging to get in.
There are websites that will announce which programs have PGY-2s open. I don't remember any offhand, but if you find it, you will be against several applicants.
My suggestion is to call up several programs. If you have to call a hundred or more then do it. At least email them. This will be easier because you can send a form letter. Ask if they have a position open, and if they do, ask what you need to do to get into that program. I wouldn't push the issue too hard. Reason being is that you want the PC on your side. I've seen several cases where applicants called the PC several times a day with annoying requests because that person was scared, anxious and frustrated. Several applicants do not see the PC as a person in power. Dead wrong. In business the secretary is usually the gatekeeper to the boss. You tick off the PC, that PC is going to tell the PD that the "applicant seems to have issues. We got plenty of other people who want this position. I say throw this candidate out."
Most PCs I've seen in programs are the Scotty (Trek reference) of the department. No the person is not a doctor, but the PC is usually the lynchpin of the residency program's operations.
As for FP, yes you can do some psychiatry in it, but the extreme and sophistication will most likely not be on the same order as that of a psychiatrist.