Daycare & potty training

I have a 2.5yr old who uses the toilet amazingly at home. She will hop on up and go pee or poop no problem, we’ll have to help her get her pants down most of the time but she does the rest & we wipe. Compared to my son, who is 4, she has caught on way quicker and does great. She even does good in public and will let us know when she ask to go, or if we ask she will say yes, and not even really have to go all that much. The only trouble lately is when we have her in her car seat, she will go in there because I think she feels the safety of the pressure on her butt. But she hasn’t done that in a couple weeks because we remind her to not go in her car seat.

Anyway… so she’s at an in home daycare with literally two other kids - so 3 total. But our daycare lady refuses to take the pull up off her so obviously she just goes in that… our daycare lady always says “she doesn’t tell me” & “I can’t have her going all over the house”. Like okay I get it, but I tell her she’s just going to keep going in the pull up because she knows she can (my son did the exact same thing). Also, I think the kids are kind of scared of her (my son literally never told her when he had to go, he’s in preschool now and tells his teachers).

Like my daughter is extremely good at toileting & doesn’t like the feeling of that in her pants. If she just got over having a couple accidents she would be good to go after that but god forbid that ever happen. Has anyone else had this issue? She has 2 other kids so it’s not like it’s a huge hassle… also she doesn’t let the kids just run to the bathroom to get started. At our house she runs to the bathroom and says “I have to go pee/poop!” And we follow her in to help get her pants down. Is it time for a daycare change? I know she’ll have to wear pull ups but maybe she’ll have more freedom & feel more comfortable with a different provider? We were looking at preschool programs. Idk. I’m at a loss.