You mentioned that mom speaks very little English. Assume they speak to the child very rarely at home in English. While she may understand the words from when they try to speak it she is used to another language. That will take time for her to adjust to. You might try to find out how much English they use at home and if not then what the words are for bathroom issues she uses at home and allow her to use them at daycare. As long as you know what they are you can react to them just the same.

Glad to hear that the agency is working on your side as far as the pullups goes. One of the reasons I left an agency many years ago was because they went out of their way to please the parents at my expense when I felt I was paying them a daily portion of my pay to be on my side or at least to not take sides and just resolve issues.