Yeah, I defiantly don't think that this is appropriate. I don't think that it should be assumed that everyone who comes to your party bring a gift. Especially once your kids are older (I see yours are 7) there are so many parties that kids are invited to that sometimes I would think that parents can only afford smaller gifts.
If I were to receive an invitation with a "registered at...." among the 25-30 other ones that I received from my child’s class at school, that invite would defiantly be discarded.
FYI- I didn't even put where I registered on my wedding invites, if people asked, I told them. You should want people to come and celebrate your marriage/birthday with you, not just "what did ya get me?"