I find it shocking to hear parents express cavalier attitudes about the importance of school. A school is a school. They all teach the same stuff. That youngster has attended three different kindergartens in the first 3 months of his educational experience. I can hardly wait to hear this mother criticize the school system when this child does poorly or drops out.
Consistency IS important.
A school is more than a building. It is friends and teachers and staff with whom the child feels safe and comfortable so he can invest his time and energy in the hard task of learning. What ever school the children attended last year, they should attend again this year unless BOTH parents agree otherwise. If paying for private school is the problem, lawyers, judges and courts cannot fix it. Private school is often a casualty of divorce economics.