My daughter is 3 and goes to a Montessori School twice a week. Can we claim the fees we pay?

Yes, you can claim it as child care if you use preschool as child care. 

The child and dependent care credit only applies if the care is provided so that you (and your spouse if married) can work.  If you don't work, the care is not eligible for the credit.

Any care provided below kindergarten level is eligible for the credit (if it is so you can work) even if the care is also educational.

You can only claim the preK expense if it is so you  can work.  Otherwise it is a personal expense.