So it seems, the Daycare is sabotaging her?
Or they seem to 'insult' your child because your child is coming home saying "she says I'm a baby Mommy... I wear diapers at Daycare...."
Degrading a child that way and calling them names, is a HUGE bad thing.
So on that fact alone, I would choose a more hospitable Daycare.
IF any Provider/Teacher called my child names... degrading them, for simple biological errors, I would be pissed. I would pull my child out of there.
That is mean.
Now, all kids are different per potty readiness or ability.
It can take time.
But at home you said she IS, able?
But still, it is still ongoing... which is also normal and common.
They are not rocket scientists about it, yet.
As for night time dryness though... night time is COMPLETELY different than daytime pottying. Night Time "dryness" is not something that is BIOLOGICALLY attained, until even 7 years old and this is normal and per Pediatricians. Night Time dryness, is about the organ development/bladder/brain/nerve connections. Not age.
It seems she needs encouragement, which she is NOT getting at the Daycare. They don't help matters.
They don't seem real kid friendly, at all.
The Daycare is the problem.
Not your child.
Also, she is among younger children, at the Daycare.
Thus, she acts/talks like them. Which is common.
An alternative is, besides "Preschool" is to find a "Playschool" type place. At places like this, it is not as hardcore and they do do 'teaching' to the children, but also, ACCEPT the child for who they are and will help with toileting. Which your Daycare, is not doing.
My son went to a Preschool/Playschool type school. They taught some academics/circle time/concepts.... but ALSO accepted kids in diapers at ANY age... and helped in transitioning a child to the toilet. My son was not completely toilet perfect yet, when he attended at 4 years old. And then he was... while there. And now at 5, he is proficient.
But my son, did pottying... very gradually. I went by his cues.
And kids still do have accidents at this age and Preschool and Kindergarten and even in 1st Grade. My Daughter's teachers all told me this.
Anyway, your daughter is young.
A child will become proficient at the toilet, when they are ready and when their physiological cues, are in place.