Problem #1 of course being, why is a Catholic marrying an unbaptized person in the first place.
No kidding. But the Church grants a dispensation in such cases if the promise is made to bring up the kids Catholic. And on top of it all, there is confusion regarding the "Internal Forum" thing, particularly since the recent papal comments regarding the Orthodox, etc. So my brother, who was deserted by his first wife and is in a second (civil only) marriage now thinks it's o.k. to receive Communion. It would be nice if he could straighten out his situation for the sake of his kids.