Hi! And welcome to our community!
One part of the Down Syndrome diagnosis is stubbornness and self directedness, so it’s not unusual for that type of behavior to appear during sessions.
Not sure what the child’s cognitive level is, but a picture schedule might be a good option- you and she alternate picking activities, but it’s all drawn out so it’s known what’s expected.
I have also found that in therapy sessions, sometimes we have to ignore or work with the behaviors rather than trying to change them. For example if the child drops to the floor and won’t stand up, sit down with her and start doing a floor activity or rolling a ball. It sometimes works, sometimes doesn’t, but it’s about focusing on what the goals of the session are- Behavior modification or therapy goals.
I don’t have any recommendations regarding the food. I know many children like milk because it’s very pacifying. Maybe if the parents offer the milk in a different cup than her usual so it’s less of an emotional support? It’s just an idea, I’m not really sure.
It’s probably also worth a conversation with her pediatrician to see what suggestions they have or how much milk is appropriate for her. If the picture schedule works during sessions, maybe a meal/milk schedule could be an option