As a frequent babysitter I would tell you that it is not acceptable to ask a babysitter to clean your house. A good babysitter has the same creed you had, “Leave the place better than you found it,” and should not have to be told. I would clean out of consideration, to help out, and to do something extra- but it is not required of a babysitter, and once in a while I’m just not up to it.
What you tell a babysitter you will pay is a “base pay,” unless you have prior arrangements with the sitter. If I tell a babysitter I will pay $5.00 p/h and they straighten up and make the house look a little better I pay $6.00 because they exceeded my expectations (just looking after the little one). If I come home to brownies on the table, a clean house, she’s reading to my son, and he’s begging her not to leave- $7.00- $8.00 per hour. Keep her. However, a good babysitter also understands not being able to afford to pay that much- especially consistently. A parent should also understand the value of such a sitter.
Note- just because you pay a babysitter $8.00 an hour once or a few times does not mean that you must continue at that rate. What you told her is what is expected. If you can’t afford to pay her more, even if she does clean up, clean your house before she comes.
If you feel you are paying her more than she is worth right now, you may leave a list of expectations along with the emergency numbers and baby’s schedule. A checklist mixed in with the schedule that includes something like, “Please make sure dishes are rinsed and washed after meals,” and “help little Arianna put away her toys before nap time.”
IF this person is your friend as well as your sitter, you should be able to sit and talk with her as a friend, about needing a little extra help around the house and feeling like you are helping her out too, not just the other way around. I would never do this with just a sitter, but probably would with a friend.
I am surely not the authority on babysitters, but I have been one frequently and have engaged them often (and find that it's a little different in each place) now that I have my own children. Ask your friends about rates where you are. I hope this helps.