Hi D.,
I am still a SAHM, with 4 children, 18 and going into college, 16, 8 and 2 1/2. I work part-time, but am able to take my little one with me, until she starts school.
We are working on potty training now, and some days it seems to go well, others, not so good. I am taking it one day at a time.
Your daycare, or the people you talk to, are probably not all that impressed that your daughter is going on the potty so soon in life. Nor are they there to do the training. When she has accidents, it is more of a mess for them to clean up. So, I would suggest talking to your daughter (if she is old enough to be potty trained, she should be old enough to talk to, and for her to understand, if she doesnt understand a conversation, she is too young to be trained). Tell your daughter that she is being a big girl and doing well on the potty, and she has to keep that up at daycare. Send her to daycare in a pull-up, they should be easy enough for her to take down by herself, and can take an accident without much mess.
Continue with the training at home, expect her to have setbacks. My little girl runs around with no pants on, to remind her that she has to go on the potty. If I forget to take off her diaper, that she sleeps in at night, she wont take it off herself.
Your daughter is testing her boundaries with you, if she can go most of the day in dry underpants, she should be able to do it at daycare. Talk to someone there, see if they will make an effort to take her to the potty a couple times during the day. If they do that, she may not have accidents, and can continue with the progress you have already made.
If they are unwilling to remind her to go, or take her, then the work is on you to do it yourself. And if she is not remembering on her own to go to the potty, she may be still too young. Potty training doesnt count when they cant do it themselves!! That is what it is all about, going by themselves, remembering by themselves that they should be going on the potty, not someone else reminding them to go.
I had to be a downer on something you thought was such a good thing as your daughter being potty trained so young, but again, if she cant remember to go on her own or do it by herself, she's not trained. And all of your progress means nothing if you have to remind her to go on the potty.
Sorry, but good luck with the daycare and potty training. Talk to them and see what they are willing to do to help you with training.