Splitting time between 3 places with young children.

We have 2 young children and currently split time between NY/TX/WY. Our kids are not in school yet so we want to move around before we are constrained by school schedules. We have homes in each place and travel comfortably (often fly private to make it easier to transport all the stuff). I’m curious if anyone in this sub has done this and what you did for childcare. We usually stay in each place for at least a couple months, find a part time nanny but then have to leave them behind and start over. How do you find childcare that is willing to move all over with you? Is this legal with an au pair? Any services that specialize in placing childcare professionals in this type of situation? Any insight from others who have done this would be awesome. Thank you!