Stephani, I absolutely do understand!!!! Lived this situation myself. The senior tech was a control-freak and this was because he was afraid someone would come along who would show him up; he was insecure. I remember leaving the property to go make a deposit and coming back to find the tech's keys on the desk and the senior tech looking sheepish saying, "I don't know what happened!" After that kept happening, I figured it out.
The problem for you may be that this supervisor does not really complain about being on-call 24/7, completes his work orders and all the Residents love him. Right? Yeah, but he doesn't play well with others though. It is really frustrating because in essence you do become the maintenance supervisor, too. So, then you have to decide how to make the team work.
You will have to assume the leadership role and it will happen when you bring the two into the office, sit them down, and point out that you need the team to work together. You will then assign duties and make it clear to both that the trash must be picked up EVERY day and then the weekly Game Plan must be met (turns completed, etc.) I assume the supervisor orders supplies and decided which turns are done when. Then dismiss the tech to go to work and have the supervisor remain. It would be best if you have a RPM or whoever your supervisor is, too, and then tell the lead guy what his "new" job responsibilies are. Present it to him as a step up, and with that comes the role of maintenance leader and trainer. Maybe he should receive a bonus or other reward, like an extra day off, a weekend off without the pager, etc. IF he completes the company's and your goals.
For some reason it works like this with guys: the more there are, the better they are able to work together as a team. When there are only two, there are problems. Thoughts?