She's catholic and the ceremony is in a Catholic Church. The reception, however, is in a hotel function room.

I agree with talking to her face to face - as nervous as I may be to do it!!
As a catholic I can honestly say that the church fully supports breastfeeding. I personally have had various different priests and bishops from different parishes come up to me after services and tell me how fabulous it has been to see me breastfeeding during the service.