I have struggled with this too: My parents are Catholic, but I am no longer. I haven't had a lot of pressure (not too much anyway), but I did have a lot of guilt about it.
I wasn't in the same boat, with my parents wanting to watch the kids overnight on Saturday (they live too far away for that). However, I think that if you want to continue to allow her to have your daughter over night on Saturdays, you're going to have to confront this. Or, if you avoid it, and your mom pushes you, you may have to confront it.
For me, it helped that I was attending a church (Unitarian Universalist) and explained that that was where it felt the most right, and I shared with my mom the 7 principles of UUs, and that it welcomed all religions and teaches no specific creed (just focuses on the 7 principles (the first is "recognizing the inherent worth & dignity over every person, etc.), http://www.uua.org/visitors/6798.shtml). The fact that I was/am still striving to become a better person and to help others through a church community meant a lot to her. I did also help that even as a child, I occasionally openly questions the Church's teachings (when I was a kid, one of the best teachers in our preschool, whom I remembered and saw occasionally in grade school, was Hindu, and she was one of the nicest, kindest, most generous people I've ever known. And I remember asking my mom about whether she was going to go to heaven, because she wasn't Catholic, and my mom saying that she thought all good people go to heaven, but it might be easier if you believe in God to be good.)
One thing I will say is that if you have to confront it, be respectful of their beliefs and say, "Mom, Dad, I respect that you are Catholics and follow the Catholic faith, but I have thought and prayed about this, and that is not where I belong. And I do not feel that that is where my daughter belongs. You can disagree with me, but I do not want her going to Catholic services. I'm sorry if this disappoints you but it is not open for discussion."
Don't let yourself get drawn into arguments masquerading as discussions--if they are not listening to you, and willing to think about where you're coming from, or automatically assume that you're wrong, then it's not going to be a discussion, and it's better to just end it.
If your mom is one of the (many) Catholics who feel that women are still, and wrongly, treated as second class citizens of the church, that priests should be married, and that the pope is not infallible, she may be more understanding than you think, and church may be at least as social as it is religious (in which case, offer to host your mom and her church friends for a visit/brunch after church, so that she can show off her grandchild, whom she obviously loves. :)