As we all know when people get married, some of them will end up being divorced.

Do foreign women have to change their visa status if they are divorced from their Thai husband?

If they are on a visa entry of 90 days, nothing changes. if th divorce and are on a 1 year extension of stay from immirgation, the permission to stay ends the day they divorce and they have to leave the country or find another reason under which they can stay in the country.

What a mess this could end up in. Does it follow that if she has children in Thailand and for any reason is unable to remove them from Thailand, then she has to leave them with the father? And that is it

She would be the mother of Thai citizens and could apply for an extension based on supporting a Thai minor child

That may require the child be living with her and she have bank deposit of 400k so could be a serious issue I suspect if not spelled out in divorce paperwork. But obtaining visa for 90 day stay visits should not be much of a problem (other than the obvious travel). I suspect for most in such position work would be a requirement and extension of stay could be arranged on that basis.