Hi there,
I am hoping I can post here without coming across as a know it all OR hurting your feelings.
My MOTHER sounds like your MIL, to a "T" I am 35 and I still don't deal with her ideally at times.
1. Your DD is first priority. You need to place her in whatever school you feel is best for HER.. not your MIL..
you can work out the travel issues...
2. Your MIL sounds very passive aggressive. She cannot say what she means, but makes herself loud and clear through actions. ( ie. doesn't want to tell you to put DD in a Church based school, but I bet if you decided to send her there, she would change her mind about driving in winter.) She is manipulating your decision ( or trying ) by her actions. You won't get her to voice an opinion, because she can't.
I agree with some of the above posters, as you get more experienced in parenting, letting other's opinions slide and putting your own first gets easier. Just keep putting DD needs ahead of everyone elses!
JBR