My college student that lives with me has a child that she claims and supports with a part time job. If she claims her child and EIC can I claim her as a dependent or not

If your college student claims her child and the Earned Income Credit (EIC), you cannot likely claim her as a dependent.

General rules for dependents

These rules generally apply to all dependents:

• A dependent must be a U.S. citizen, resident alien or national or a resident of Canada or Mexico
• A person can't be claimed as a dependent on more than one tax return, with rare exceptions
• A dependent can't claim a dependent on their own tax return
• You can't claim your spouse as a dependent if you file jointly
• A dependent must be a qualifying child or qualifying relative

See IRS article here.