Assuming upon divorce (or split) this is Dad's home, his home where he spends time part of the year, not mom's. It isn't always as simple as it appears when a couple with kids breaks up. I don't know that we need to know all about the situation surrounding why the parents aren't together anymore nor how they split their finances, equity, etc. (which falls under who owns what home).
It isn't something that should nor needs to be public. I know, personally, it is very trying and you do what you have to in order to care for your children. I don't see anything alarming with moving around, especially as a single mom with 2 kids. Moving sucks in these situations so what I say is...GO ZENYA! She must be one tough cookie, she sure is doing an amazing job in this horrible situation.
I agree that moving sucks. That's why I'm not doing again until I retire. It's a lot of work and costs a lot of money.
Since RH doesn't live there full time, you'd think he'd want to make a traumatizing event easy on the kids. Let them stay in their home. Cause less upheaval. I'm sure ZH can't afford it on her own, so maybe that's why she had to leave. The house is a bit remote so AH wouldn't have the option of walking to school either.
Just trying to look at other items that haven't been discussed....