Daughter and three children

You cannot claim the support you provided, but you might be able to claim both her and her children as your dependents.  How much was her 2020 income (including any unemployment comp)?

No.

As you said, she already "claims her children on her tax refund".  A person, adult or child, can only be claimed on one tax return.

A child can be the “qualifying child” dependent of any close relative in the household. Since they live with you, it may be better if you claim one or more of her children, INSTEAD of her claiming them.  It may be worthwhile doing trial returns several ways before filing.

It's essentially optional, who claims the children (her option, not yours). But for you to claim them, you must have a higher income than her. 

Doing test returns is easier with download TurboTax (TT) than using online.  Instead, you can also Try this tool https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1. 

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There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

.A child closely related to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled
2. He did not provide more than 1/2 his own support
3. He lived with the relative (including temporary absences) for more than half the year
4. He is younger than the relative (not applicable for a disabled child)
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
6. If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

@gailfree - the subject can be complex.  best to just run your scenario through the IRS's dependent tool

I suggest running it twice:  a) answer the questions as if you wanted to claim everyone and b) play the role of your daughter and see what happens.

https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent