Paying mother for childcare

I am paying my mother 250 $ / week to baby sit my daughter and also to help my wife at home ( it is hard to give her the money but I feel better this way ). This makes her income of around 12000 $ / year. 
Can i claim that as a "child care credit" when I do my taxes ? Do I have to file her taxes such as Social security, Medicare etc ? How can I do that ? 

Also does she have to file taxes on her income ? how can she do  that ?