Yes it is a good idea to have your case ready for your MILon the reasons why your DD should stay where she is
one is be honest about the subsidy arrangement at the other daycare until you finish college
another is it is easier to have a special relationship with her grand child when she sees her on her special visits to her house rather then see her everyday
right now she is happy and use to the routine of the other daycare and has friends there ou BUT IN THE FUTURE when she may be going to school it may a good time to have here as a before and after school and you are working