I have previously done child care in my home. So my opinion comes from a provider's viewpoint, as well as a parent's. As a mom, I know how much it helps out being able to claim any and all childcare/school expenses. So, when I was watching children, I always made it an option that was 100% up to the family. My thoughts were if I am earining an income, I should technically have to claim it. I know there are home providers who REFUSE to allow families to claim it on their taxes, and personally, it makes me a little weary. With her allowing you to claim it, and therefore having to claim taxes, she too can write other stuff off, such as gas mileage, and expenses for your child(ren) for any trips, meals, etc. Yeah, she may end up having to pay some taxes, but it is only fair that you be able to claim it, since you are the one putting out the money for your child's care.
Good luck and congrats on the new baby!!