In our conversation, I offered to them, that if the estimate came back too high, that I'd be willing to carry some of the cost for a short term and that she could just pay an additional payment with the monthly rent until the entire balance was paid if that would help. 

Stress to her that you've got 30 days to get her security deposit back to her and once your handyman (or some other fictitious person) walks the unit and reports back to you on necessary repairs you'll be sure to mail the balance of the deposit to her.

I am no lawyer or CPA, so don't believe a word I say and check it with professionals and people who have done it first (all I wrote below is taken from reading, so just assume I don't know what I am talking about ;-)), but my understanding is:- the biggest challenge is the due on sale clause (that gives the bank the right to charge the balance on sale).

He agreed to pay $600 towards the rent while his daughter and boyfriend take care of of the balance.

Don't see why you would treat this differently; just take the monthly rent and the cost of a new tentant out of whatever balance they haven't used.

If they don't pay the power company will go after the tenants for the unpaid balance.

I think 14 days gives a nice balance between "Its none of your business who is staying in the apartment I am paying rent for", and your side "I am paying more money for utilities than was originally agreed upon" I definitely understand your concern regarding utilities that you pay for- that is something I failed to think of when I was writing my post.

And not all of them are going to come off, and you shouldn't care about that.What you should care about is creating new positive marks that create enough points to bump up your FICO score.The best advice on keeping your Credit Rating Strong is this artice from MyFICO.comhttp://www.myfico.com/CreditEducation/ImproveYourS...On your credit cards it's important to understand that just a couple of cards with balances that are 30 to 40% of maximum, that are paid on time over 24 months will really help your score.

They are not even listed on a balance sheet anywhere.

Have them set it up to pay off in full every month so you never carry over a balance.