Because when they go to school they will have a different family name
How are their school friends going to know that their surname differs from their mothers and their step fathers.
I didn't change my name when I got married so I have a different surname than my children, even the worst school bully would not be aware of it.
My kids school has a number of kids with single parents, parents re-married, siblings with different fathers. The other kids don't even notice.
She can't change the birth certs of her children and her new husband can't adopt them without their father consent, so she probably cant legally change her kids names anyway.
If they start using their step fathers surnames, will they be able to get a passport in this name, or will it have to be in their legal surname as per birth cert.
There are a number of issues to decide before changing their kids surnames.
Her ex-husband is still the childrens father, except in expectional circumstances, he has a say in all this as well.