I'd explain the situation, saying that due to financial constraints a line had to be drawn somewhere, and the bride, the groom and the people footing the bill for the reception decided that it would be an ADULTS ONLY event.
Since he insists on being an immature brat about the whole thing, he can easily be UNINVITED so his wife can attend and he can stay home with the kid. I'll bet the kid isn't *that* well behaved that the dad can handle him for a whole evening. Obviously, if they can't nail down a babysitter, the kid is a problem, or he's just too cheap to pay for one.
Alternatively, inform him that if he's willing to pitch in the extra money (make it unreasonably expensive, say $2000) to cover the cost of ALL the children being invited, the decision stands that the reception is ADULTS ONLY. Have some ushers on greeter duty at the reception entrance to do the dirty work, and give them some extra perks to ensure that nobody who brings kids will be admitted [but don't broadcast this beforehand].
Another option would be to just say, "Oh dear, I would think that, as an Elder™ you would follow the Society's recommendation and not try to impose your demands on the host of the wedding by trying to bring more people than were invited. How rude!!" I believe the reference is in the 1984 Watchtower... somewhere between April and June. It was current around the time Mr Scully and I were planning our wedding.