It's a matter of Head of Household status.
For your mom to be able to claim the kids on her return there's some qualifications that need to be made. Publication 501 by the IRS has the details.
To qualify:
The kids can't be claimed by anyone else.
Kids must be related to the taxpayer (sounds like they are).
The kid's gross income for the year must be less than $3,300.
The taxpayer must provide more than half of the kid's total support for the year.
Kids must be under 19 years old


