My mother lives with me and is paid to care for my baby while I work. Can I claim her as a dependant even if I paid her a modest salary?

You cannot claim your mother as a "dependant", (unless she is dependent on you for support by reason of infirmity).

You can, however, claim the childcare expenses you paid to her, and she must include what she has earned on her own tax return as income. 

Some more information from TurboTax regarding Childcare Expenses can be found at this link: https://bit.ly/2u0zNqq