does mom have income? if not, she doesn't file.
it would seem that the children would be qualifying children for both your mother and you since the only support test is that the children don't provide over 1/2 their own support. the normal tie-breaking rules for claiming a qualifying child is that the parent gets the child. there's an exception to that. if an individual's parents can claim the individual as a qualifying child but no parent does, another taxpayer may claim the individual as a qualifying child, but only if that taxpayer's AGI is higher than the highest AGI of any parent of the individual
here are the requirements to be a qualifying child
Qualifying child
1) Related
2) Same principal abode as taxpayer for more than ½ the tax year. Temporary absences like for school are ignored
3) If not a full-time student, under 19 at the end of the tax year. If a full-time student under 24 at end of tax year.
Full -time means an individual who during each of 5 calendar months during the calendar year in which the taxable year of the taxpayer begins is a full-time student at an educational organization described in section 170(b)(1)(A)(ii), or is pursuing a full-time course of institutional on-farm training under the supervision of an accredited agent of an educational organization described in or of a State or political subdivision of a State.
4) Hasn’t provided over ½ his/her own support
