If your partner is anything like my ex, he will have denied your right to rest and criticised you for needing it.
You are entitled to rest, if that is what you need. Abusers make us think we need to be hamsters on the wheel, going all the time. Resting doesn’t make you an unfit mother.
You may find the separation means your migraines improve- who knows- but in any case, it’s important that children learn empathy and give allowances to parents, especially those with health problems.
You will be able to set up your own routine where everyone is taken care of, with the bully out of the way!