Its hard to offer advice from outside the province because we are all in slightly different situations.
I have been closed since Monday 16th March. I also have client's paying a portion of fees however, I know that for many, they are struggling to pay this when they are not receiving service. It's one of those hard situations that are very unique.
Today, I got notice from a client I would never have guessed I would lose. Out of my 6, I have one going on mat leave in June and two Dads who have been laid off, but this one I lost, I didn't expect to loose. Mom has been on mat leave almost a year, which ends in June so I didn't expect to lose them 11th.
I don't think your client is taking advantage. She's doing what she can to keep her child safe and still paying for the spot - as you said, you chose to reduce the fees and she has been paying and continues to pay. I think she's been more than fair.
If you aren't happy with it, give her notice and find someone else - but bear in mind, someone new coming in, who you don't know has been socially distancing is a big risk and odds are, you won't be able to fill that space until this is behind us anyway. It's going to be late June before life has some level of normal.