I would be really irritated if I was in your situation. I personally don't think your late fee is high enough and I think you should talk to her in a calm but firm way and explain that your closing time is firm and that it is not fair to you, your children or her child when she doesn't come on time. Explain that you work a very long day and it is not fair to you to be left wondering at the end I everyday whether or not she will be on time. You have the right to make plans in the evening without having to worry about whether a client will be on time. What if you were going out or had company coming over? It sounds like she thinks she can be late and pay the fee and that solves the problem, but I think you need to let her know that it is not okay. Mind you, if you are okay with increasing your hours for her the tell her that but definitely charge extra and set that schedule in advance.
My late fee is $20 per every 5 minutes of lateness and that is to act as a deterrent. I have had one parent about five minutes late in a year and she texted me 20 minutes before I closed to let me know she had been caught up at work. Personally, my evenings are very hectic once school and my kid sports start and I have to run a tight schedule to avoid being late for my own family obligations.