Yes, you can, but there are some rules you need to understand and follow.
First, if your daughter wants to claim the child, she has the absolute right to do so regardless of support or anything else, because she is the child's mother.
Assuming your daughter agrees to not claim the child, then these are the rules you follow:
1. You can claim your daughter only if her taxable income is less than $5050 and you pay more than half her support, OR, she is a full time student under age 24 and lived in your home more than half the year.
From your information, it seems most likely that you can't claim your daughter. Your daughter does not have to check "someone else will claim me" if this is the case.
2. You can claim your grandchild if:
a. your daughter agrees not to claim her
b. your taxable income is higher than your daughter's taxable income,
c. your grandchild lived in your home more than half the year OR your grandchild lived in your home less than half the year but you paid more than half the grandchild's total support.
You should first look at your daughter's status. If you can't claim her, as I suspect, then you should each try claiming the child (on a test tax return only) and see who gets a better refund or lower taxes. If you are the person who pays more than half the total household expenses, you can claim the child and then file as head of household, which has lower rates. If your income is from working, you would qualify for the child tax credit up to $2000, but if you are retired and your income is not from working, you won't get that credit. Your daughter would file as single. If your daughter claims the child, she can't file as head of household if she doesn't pay more than half the total household expenses, but she might qualify for a partial child tax credit and earned income credit, depending on her income.
Bottom line, you could claim the grandchild. You probably can't claim your daughter if she works full time. But to know which is the best combination, you would have to test the different options. Then file according to the best option.
