I have no income for the year of 2020 because I'm a stay at home mother. Can my mother whose been living with us for over a year claim my two children for me?

[macuser_22]

Probably if you are not required to fie a tax return and the other parent did not also live with the child(ren).

Qualifying Child of More Than One Person

[Quote from IRS Publication 501]
Sometimes, a child meets the relationship, age, residency, support, and joint return tests to be a qualifying child of more than one person. Although the child is a qualifying child of each of these persons, only one person can actually treat the child as a qualifying child to take all of the following tax benefits (provided the person is eligible for each benefit).

1. The child tax credit or credit for other dependents.
2. Head of household filing status.
3. The credit for child and dependent care expenses.
4. The exclusion from income for dependent care benefits.
5. The earned income credit.

The other person can’t take any of these benefits based on this qualifying child. In other words, you and the other person can’t agree to divide these tax benefits between you.

Tiebreaker rules.

To determine which person can treat the child as a qualifying child to claim these five tax benefits, the following tiebreaker rules apply.

1 - If only one of the persons is the child's parent, the child is treated as the qualifying child of the parent.

2 - If the parents file a joint return together and can claim the child as a qualifying child, the child is treated as the qualifying child of the parents.

3 - If the parents don't file a joint return together but both parents claim the child as a qualifying child, the IRS will treat the child as the qualifying child of the parent with whom the child lived for the longer period of time during the year. If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year.

4- If no parent can claim the child as a qualifying child, the child is treated as the qualifying child of the person who had the highest AGI for the year.

5 - If a parent can claim the child as a qualifying child but no parent does so claim the child, the child is treated as the qualifying child of the person who had the highest AGI for the year, but only if that person's AGI is higher than the highest AGI of any of the child's parents who can claim the child.

Subject to these tiebreaker rules, you and the other person may be able to choose which of you claims the child as a qualifying child.
[end quote]

https://www.irs.gov/publications/p501#en_US_2018_publink1000220917

[VolvoGirl]

If you are not married or not living with your spouse she can probably claim you too.  If you are married it is best to file a Joint return even if one spouse has no income and claim the children on the Joint return.

[Anonymous]

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