H.H.
They should NOT put her in diapers for an accident. Kids of all ages have accidents.
There is a good chance they will teach her how to sit on a big potty or that they have little potties just for toddlers. I would look into that. That being said, I think it's perfectly reasonable for them to use your little potty seat (especially if you have one of those little portable ones!).
Also, they throw that term "health code violation" around easily. Many places don't actually know. Read up on it yourself. We cloth diaper and I have a friend that wanted to cloth diaper but her daughter was going to daycare and they told her it was a health code violation. Turns out, it isn't. Many daycares automatically say that about cloth diapering, so I can imagine potty seats could be similar. I don't know the law (we don't go to daycare), but I would check it myself if I were you and not just accept "health code violation" as an excuse until you know that law.