I would let her know that in the several months since the interview you have had to make changes to your contract. I would email it to her and see what she says. If she's good with it, great!! If not, you can decide if you want to allow her the old contract.

I have had a similar situation in the past. My family that is part time only pays for 3 days a week and they pay every other stat holiday and they also pay half the fee if she is scheduled in for half a day. I have since changed that and now charge full time regardless of hours and days here and all stat holidays. The part time family I have allowed to stay that way because that is the arrangement we agreed upon when she started. None of my new families know this though....although they are all full time so it wouldn't really matter anyways.