I had a little monkey who at about 15-18mos. old was climbing out of her crib and would get her leg over the top rail and then either sucessfully climb on over or fall to the floor trying. She also slept with me alot too so that could be why she wasn't doing great in her crib. So for safety reasons I got a toddler bed. She never took to the toddler bed, it was a waste of money and has been in my bed ever since. Probaly doesn't help much but that's what I did.
I know daycare center's will leave them in a portable crib til they're transitioned over to the toddler room where they are then on a cot on the floor where it's safe.
When I worked at a inhome daycare we kept the kids in a crib or pac-n-play til about age2, then we transitioned them to a mat on the floor and it was usually when they were mature enough to learn to stay put.
I have a cousin who takes everything away at age1. Bottles, pacifiers, and the crib. She moved both her daughter's straight to big girl beds and they both do amazingly well.
Then I know plenty of people that keep their lil one's in a crib til age3.
I don't think there is exactly a right or wrong age. I did the change out of safety but would have loved to keep my "baby baby" in a crib longer.
Like right now my daughter needs a booster in the car but I'm just not ready for that so she's in a 5pt. harness and 6years old.
Do whatever you think is right and comfortable. I would be upset that your daycare lady is making big important changes for your daughter that should really be your decision not hers.
Try and talk to her that sleeping in two different types of beds is confusing and your having problems at bedtime at home and that if you could both be on the same page it would reduce stress and confusion with your child. Offer to bring a pac-n-play maybe she's had another child that needs hers and moved your child up to give the other child the pac-n-play.
Daycare is hard, I don't think it's ever exactly 100% what we want. I've had problems everywhere I've ever sent my child some problems I had to bite my tongue and just live with other's I removed my child depending on how serious it was. Right now my daughter has to much freedom at daycare and isn't supervised 100% of the time. But it's one of the best choices I have, not perfect but when I weigh the options it's better than my other choices.