When is IRS accepting refunds?

[DoninGA]

If she is not claiming the children or her tax return then you may be able to claim her and her children on your tax return as nonrelative dependents under the Qualifying Relative rules if they meet all the requirements.

You cannot have Head of Household fling status claiming either her or her children as dependents since they are not related to you.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,200 (social security does not count) in 2019
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.

[MinhT]

It depends.

You can claim the woman and her children as your dependents if they pass all of the following tests:

1. The person can't be your qualifying child or the qualifying child of any other taxpayer. 
2. The person must live with you all year as a member of your household (and your relationship must not violate local laws). 
3. The person's gross income for the year must be less than $4,200 in 2019. 
4. You must provide more than half of the person's total support for the year.
5. The person is a U.S. citizen, U.S. resident alien, U.S. national.
6. The person is not a married person who files a joint return unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid.