NJ, I'm not old enough to be entitled to State Retirement Pension an I have no wee ones but it doesn't stop me from claiming a State Pension or Child Benefit.
As you can see from your post
"If you’ve moved to the UK:
You may be able to get Child Benefit if your main home is in the UK and you have permission to live in the UK."
The important words there are "may be able to get child benefit" the fact she is British gives no automatic entleent to that it.
NAOMI, I said it was unlikely she would get Child Benefit immediately.
This link gives details of Child Benefit conditions for folk coming from abroad.
https://www.gov.uk/government/publications/child-benefit-coming-to-the-uk-or-going-abroad-factsheet-ch5-notes.
The Hab Res Test also applies to Housing Benefit claims.