My daughter is 16 and had a child 4/1/2021. They both live with me and I support them both. Will I be able to claim BOTH of them on 2021 taxes if my daughter doesn't work?

Yes.

 

For your daughter, you can claim her as a dependent if she lives in your home more than half the year, and doesn't provide more than half her own support.  She can work and still be your dependent, there is no dollar limit on her earnings, only that she provides less than half her total financial support needs.

 

For your grandchild, you can claim them as a dependent if they live in your home more than half the year, and if the mother agrees to let you claim the child, and if your income is more than the income of the child's mother (your daughter).  If the mother wants to claim her child, she gets the first right, so you need to discuss this before filing your returns.  

 

Now, depending on your overall tax situation, and if your daughter has some income earned from working, it might be that your daughter would get more money by filing as not a dependent, and claiming her daughter as a dependent, than you would lose by leaving them off your tax return.  This would have to be tested for your unique circumstances.