She sounds a bit demanding right from the get go. To say she needs something "immediately" - and then shows up late for the interview; especially on a Sunday when you have to work the next day. You are very accommodating - I must say, I would not have been so much.

If you are feeling like she's going to take advantage of you constantly, you should go with your instinct. Hopefully you can find someone else to fill the spot. Regarding her daughter hitting, did you tell her about this? what was her reaction?