Take a deep breath. They're probably sneaking food and water while you aren't in the room . If they aren't, then they will soon. When you change their food, do you see seed hulls in the dish? (You can blow gently on it- if they move easily those are seed hulls). If you see hulls, they're eating. You probably won't see them drink- they're sneaky about it
Don't try to interact with them except for changing their food and water for 2 weeks. Since they seem to be timid, you can cover three sides and the top of their cage with a sheet to make them feel more secure. In addition to that, leave a radio or TV on so that there's background noise- budgies perceive silence as danger!
Best wishes for you and your two little ones.