This is often a requirement for international travel now anyway so you probably know about it. It would be an unusual thing for children to be travelling without their mother (well here, an unusual thing to be travelling without their nanny), so to avoid raised eyebrows, I'd suggest this precaution too.

My understanding is that children and wives under a husband's sponsorship don't need exit permits and I've never heard of children ever needing an exit permit (except for my kids but that's a much different story).