Visit the Montessori school in your area as well. Ask about the success that its students have experienced when they have moved on to other schools. Visit the classrooms, ask for any printed information about the Montessori approach, and find out about the resources and opportunities your son will find there.
Many people believe strongly in homeschooling, and there may be a homeschool group in your community for parents who participate. The most successful homeschools are the ones that follow a curriculum on a regular and consistent basis. The biggest drawback to homeschools is the lack of socialization available for the children; a community group for homeschooling parents can help address that issue so that the children have opportunities to get together for joint projects.
If you feel sure that your decision is the right one for your son, stick with it. You may find it easier to convince your mother-in-law, however, if she sees that you have listened to her and investigated all of the possibilities available for your son.