I think you have gotten a lot of good responses.
I agree that MAYBE she is having trouble making ends meet, BUT if that is the case then she should talk to you about it, not just dump her kids in the driveway and take off. She KNOWS she is wrong or else she would come to the door.
speaking as someone who was once a single mom having a hard time making ends meet.....when my son was in a daycare (it was also an in home) when I was having trouble, I would talk to my daycare provider. I knew she was counting on my check every week, so if/when some week was particularly hard for me, I would talk to her about it and she would either let me pay her the next week or break it up and just make a bigger payment for a couple weeks. But I ALWAYS spoke with her about it. I never would have just dropped my son off without paying her or talking to her.
I don't know how long it has been going on for you, but you need to confront her and find out why she is not paying you. As someone else said, put it in writing. Make her an invoice showing what is past due, what she owes for the current week and what her weekly amount is. I would also attach a letter stating that she is this $$ amount past due dating back to such and such dates and that if not paid in full or payment arrangements made IN WRITING then you will no longer be available to care for her children. I would also say that future child care will need to be paid for in advance. (Make sure you keep a copy) Then, if you can't catch her in the driveway, send it to her, certified mail That way she will have to sign for it and you will get a confirmation sheet back that shows she signed for it and you will have proof that she received it. .(just ask at the post office what you need to do so that she has to sign for it and so that you can receive a confirmation sheet) You will need things like that if you have to take her to court. And when you do get to see her face to face, if she is going to continue to bring her kids and pay you, have her sign a contract showing what she is to pay and that is has to be paid a week in advance or the kids aren't allowed to stay and that SHE herself has to bring them to the door. And if she pulls the dropping them off in the driveway bit again call the police. Again, that way it is documented and you will have proof if you ever do need to go to court. It is sad that you have to be that way with people, but in some cases (some people) have to be handled that way.
It may just be that you need to put your foot down and just let her know that she cannot take advantage of you. Did she do this to her previous daycare provider? Maybe this is normal for her? If possible, find out where her kids went before coming to you. I'm guessing here, but if she is leaving them in the driveway, she has probably done this to someone else. Again, just my guess. (my husband's ex wife did something similar to a daycare lady who was watching their kids - she didn't pay and then she quit taking the kids there after the lady told her she owed for past amounts and the daycare lady called us - not to say that we owed her, but to let us know that she was going to take her to court for what she owed (as well as some other bits of info, he told her go ahead and that she had done the same thing before). I think after the daycare lady sent the letter saying that she would take it to court, the ex paid what she owed. But she was like the lady you are dealing with and I KNOW she did that to other daycare ladies too.
I'm sorry you are having to deal with someone like that and I hope that things work out and you get the money you have earned.
Okay, sorry such a long response things just kept popping in my mind as I was typing.
Prayers and hugs!
K.