It would be a bit of a dead giveaway if you tried the 'controlling the numbers' line and she turned up and there were eighty people, including partners, and it was a casual bbq. That line can work with weddings, where it is often a legitimate excuse, but is probably not as believable with a child's first birthday party.

Although if he does come, you'll probably be so busy that you won't have time to notice his douche-iness anyway. I doubt I managed to have a conversation longer than three sentences at my DS' party, so if he p*sses you off, as the host you have a pretty legitimate excuse to tend to other guests, or to your DD.