When little ones refuse certain foods, I start suspecting allergies or that their bodies are just not ready to digest that food yet. I knew a mom that thought her dd was just being difficult when she said she didn't like peanut butter, the mom insisted that she eat at least some of the sandwich, before she was done, dd was head to toe in hives.
My ds would not drink milk (even chocolate milk) without it being warmed up until he was 5yrs. Now he is 10 and won't drink white milk, in cereal or with chocolate is fine, but he won't touch straight milk. In our case, I don't think it's an allergy, but it may be a digestive thing, he tends to stay away from high acid foods in general, including most fruits.
I really don't have much of a suggestion, but to not stress about getting dd to drink milk. Just make sure she is not getting dehydrated at caregiver when the EBM is gone. Nurse at home as much as possible, maybe add unsalted butter to some of the foods she already eats to add some fat & calories.