I'd be very surprised if they had a problem with that one, but they would have no legal standing anyway as it's simply not their business name.
I don't think so. particularly not if you site isn't related to hosting, domains or any other business that godaddy is in.
The Reason I am asking this is because, gomommy.com redirects to godaddy , go-daddy.com redirects to godaddy obviously, but go-mommy's are available.