How should I handle repairs on rental home with absentee owner?

Wow! If you still want to rent from her tell her that you need proof the roof was fixed. A receipt you can verify should work. Also tell her you know that she has a record of not fixing things and that you want it in writing that things will be fixed within a month of you notifying her of a problem or you can deduct the next months rent(s) by the amount of the repair.