You might find the child does better if the highchair is pushed up to the table where she is part of the group. At this age I would be weaning her off the bottle at daycare but in this case probably would put her in the chair at snacks and meals and give her one or two pieces of food on the tray - no sense trying to chase a flying dish and leave her to scream if she insists. Then straight to bed. AFTER nap I probably would do the lay her down and have bottle if that is all she is eating. But she is not allowed to move from that spot or bottle is taken away. That might also be the way to wean her to a cup in that after nap she gets milk in a cup on the floor. Limit the amount in the cup/bottle to no more than 4 ounces - just enough as you say to stay hydrated for the day.

As far as getting her to eat you will have to let mom know that until she insists the child behave properly at home that you will have difficulties at daycare and that it is mom that has to change routines not you. In a couple months the child will be old enough to accept both routines and have a better understanding when you speak to her. Between 16-18 months you can start to enforce your rules and by then the bottle should be gone at daycare and if she wants a drink she gets in her chair properly.