You as a biological parent always have first claim to your child as a dependent. Your parent can only claim your child (their grandchild) as dependent if your child lives in your grandparents’ home more than half the nights of the year AND you give permission.
When you were not working, and because there was no stimulus and no enhanced child tax credit in previous years, it probably made financial sense for your parent to claim your child as their dependent. For 2021, with the recovery rebate (stimulus round three payment), and the enhanced child tax credit, it may now make more financial sense for you to claim your child as a dependent. The only way to know who gets the most benefit from claiming the child would be to prepare multiple tax returns that test each combination.
You should discuss this with your parent before any of you file your 2021 tax returns. Just the fact that you would be claiming your child instead of your parent should not by itself cause any trouble with the IRS.
