I'm sorry to know of your recent problems, it will get better. You should be proud that you have provided for your family this many years and never needed help before now. As a single mom that has to be tough. Even tho you don't want to, borrow what you need to get by on until things improve.
Yes, don't back down from AOL. Back a few months ago it was on the news here. One man had called to cancel his account, I believe he had tried to cancel in the past. This time he was recording his conversation with the company rep. I forget how long he was on the phone,seems like it was over 30 mins. The entire time the rep continued to try to keep the service active with different offers and such. The customer repeatedly asked for the acct to be cancelled, only to be asked in a different way to keep it open. As someone listening it got comical, the company idiot wouldn't give up!! As a customer, I would have been PO'd.
My point is AOL has recently had numerous consumer complaints about this very subject - account cancellation. The bad press on this incident was very embarrassing for them and I would think they would be quick to resolve other complaints.
Good luck hon, and don't let it get you too far down.