I would go in all guns blazing!
They have no right to make decisions like this for your child
THey have no right to judge your flaming lunch box, nor to gossip and talk bollocks about your dd.
They don't know a thing about anything, and as you've clearly said to them that the current diet she is on is reported with the medical teams she is under and the instruction is not to change anything without them knowing.
Milk - as far as I know- is more likely to cause laxative affects in intolerance than constipation. The main thing you need to do is to keep little one hydrated, that's not rocket science and by them depriving her of fluid, they are actually more likely to be affecting her health than anything else.
Go in and roar at them, write a letter of complaint and make it damned clear that THEY are absolutely out of their competence zone, and to get back to what they are good at, whatever that is, and leave you to parent your child and negotiation with medical professionals. If you have any instructions for them, you'll let them know. Until that time they need to back up and leave things as ou have them.
You have to pull her from that nursery, it's such an unprofessional setting.