I don't think your DD is overdue but I do think that you sound very tentative with your daycare. When my son started at a daycare recently (he had been in a Montessori school prior to our move), the daycare and I had a number of discussions as his caregiver and I did not quite see eye-to-eye.
We seem to be on the same page now but here is an example:
My son has been working on potty-learning off and on since he was eighteen months old. I didn't rush him 'cause he isn't going to college in diapers, ya know? He and I talked about it, and he told me he wasn't ready to use the toilet yet, though he had the mechanics down.
When we ran out of diapers, I told him I wasn't buying anymore and we would use the pull-ups only from that point until they ran out, then we would use undies; I was laid off in Feb so it was a cost-savings measure.
Well, we were running out of pull-ups too so over Memorial Day weekend we had naked time; he spent Saturday and Sunday naked. Every half-hour to an hour we would have a Pee Break and run to the bathroom. When he didn't want to go, I would then wait until there was something he wanted; "I'll be glad to read to you after you pee in the toilet." It wasn't said meanly, just matter-of-factly, and he would then run to pee in the toilet.
On Monday we added underwear to the mix so he could practice; we went to the store and picked out a bunch together. I asked his opinion and let him pick out the ones he liked, thereby vesting him in the process.
Okay, so that's the background; sorry it's so long.
Sooooo...Tuesday he goes to daycare and I told his teacher, in front of him, that, "M is now wearing underwear during the day; would you please help him when he needs to use the toilet?" He had a couple of accidents but most of the time, he peed in the toilet.
On Wednesday his teacher tells me, "I'm not trying to tell you how to raise your child, but
he had three accidents today and maybe he's not ready for underwear yet." I looked on the board and saw that he had SIX times when he managed to use the toilet, so I asked her about it and she said yes, he had used the toilet six times successfully. I told her, again in front of my boy, that he was doing well, I expected a few accidents while he learned and practiced, and he was NOT going back into pull-ups.
The rest of that week, he had precisely ZERO accidents. Since then, he's had a few but it's mostly peeing ON his shorts rather than IN them; he still has a bit of trouble getting them down far enough and there's a gap in the toilet seat so...overall, he is doing a great job!
We still have mostly naked time at home; it's easier on all concerned 'cause he is still learning his body's signals. The whole process has been pretty funny though, especially when he rushes past me in the hallway saying,
"Excuse me, Mama, I have to poo!"
P.S. The point of that whole long post
is that YOU are her parent; have strength and confidence in your decisions for her, and don't let anyone intimidate you into doing anything that YOU feel detrimental to her.