Would you fire a daycare client because they are accusing you of making their child fat?

I've been watching this particular child (20 months) for 6 weeks. She has always been a heavier child. This is not new or changing.

Her mom decided she would provide her own food and drinks. I charge $50/week more for breakfast, lunch, milk, and two snacks.

This mom told me that she was at the doctor's on Wednesday and her 20 month old daughter has a diagnosis of childhood obesity. She claims her daughter has gained ten pounds since starting with me. She packs her daughter junk to eat and juice. I told her when she started that I wasn't trying to be judgemental, but she should pack more healthy options vs SunnyD and Doritos/Cheetos and Oreos. She told me that she will pack her what she packs her and it's not my business. This kid eats fast food at least two or three times each week that her mom sends via doordash.

The mom got pretty hostile with me and told me to stay in my lane at the time I mentioned diet. When she was talking to me about her daughter's weight yesterday, I said I would be more than willing to serve her what I serve the other kids and I gave her the monthly menu, but she told me not to tell her what to feed her child. She told me her toddler doesn't need to go on a diet. She said she was just telling me that this is the first time her daughter's weight has ever been a concern and "you're the only new thing that's come along".

I told her that I give her daughter what she sends to eat. I don't give her anything else. If she doesn't want to send different food, and she doesn't want me to feed her daughter what I feed the other kids, then I don't know what she wants me to do!

She called and left a voicemail where she was yelling at me and I'm like... I can't deal with this. Pickup is at 6pm and I'm trying to figure out how to tell her that she is not welcome back on Monday. She's paid up to the end of April but I absolutely will refund her for the final days (since she paid today and I'm firing her today).

Has anyone had this happen? How do you deal with it?

Edit: She was 30 mins late to pickup (another problem that's been ongoing). I sent her a message (text) at 6:15 saying that effective immediately, she is no longer a client of mine and after she picks up her daughter, she is not welcome or allowed on my premises any more due to her behavior.

She told me she is calling the police on me because she has "plenty of evidence" and I said I await their arrival. I'm not scared. She can lie all she wants.

She signed an agreement that fees are not refundable in case of client termination. She will not be out money since she paid today for the remainder of April, but I'm refunding her since I fired her today and she already paid this morning. If I didn't refund her, I would feel icky about that. If it had been sometime next week, I would feel differently.

She signed a contract when she started stating all this and I have everything in writing with her signature on it. She also has copies (digital and hard copies) of everything. There is a piece in there about behaviors/conditions that result in instant termination and yelling is clearly on there.

She left me another voicemail but at this point I have blocked her and told her that if she continues, the police will be called. I have cameras so I'm not too worried.