S.T.
I'm not going to make a negative statement so please understand. I'm going to make a practical one.
Friendship ends where money is concerned.
In other words, the house is the homeowner's ultimate responsibility. The renting of the house comes with responsibilities as well for the homeowner. One is to maintain the electrical system if there was no problem caused by the rentors (you guys). I suggest reading up on the landlord laws for GA as this is always good information to know before going into any renting contract with ANYONE.
Push the fact that she's family to the very back of your mind. It's not practical to consider feelings when you're dealing with contractual issues such as renting. It's business and always will be. She knows this. She also knew the A/C was probably going to go out but was putting off replacing it.
Get 5 estimates on replacement for the unit. NOT REPAIR. Replacement. Repair on an old unit is worthless. I speak from experience as we've just dropped the repair bills on our unit and opted to buy a whole new one instead and we don't regret it a bit.
Give her a copy of the estimates and all of you sit down and discuss this at a neutral location such as a restaurant. Emotions won't run as high at a restaurant and you can have a peaceful, logical discussion. Get her agreement to pay for the replacement and the payback to you guys from your rent IN WRITING, whether you feel comfortable with that or not. It will protect you!
After the unit is replaced, start taking out the replacement costs from your rent. KEEP VERY ACCURATE RECORDS! If SHE agrees to replace it with her own money, tie her down to an exact date and hold her to it. Let her know that if the unit isn't replaced by this date, you'll have it replaced yourself and will take it out of the rent payments. Get everything in writing! Make absolutely sure you PAY YOUR RENT ON TIME. You don't want her to have reason to give you a negative reference or be spiteful about things. You should never give anyone a reason to make things harder on yourselves in the longrun.
Legally, rentors cannot "hold the rent" on an agreement without solid WRITTEN evidence that a contract has been broken. You really should read up on the GA landlord laws.
You have a BUSINESS deal and all parties should act responsibly about it.