Hi prudence
Please don't think we're ignoring you. There must be more people than I thought who felt, as I did, unsuited to give advice on this. But I'll step up and give you what I can.
I feel for you. I had to organize a party for my mother's 80th birthday, inviting family, neighbours and friends old and new. Sending out the invitations was tough (what if miss somebody? or invite someone inappropriately? etc), but the days leading up to the party were also filled with worry about not recognizing people who I really should know, or not remembering names, or saying something stupid... my anxiety was so high that I think I actually dissociated during the party because I don't remember much of it.
Despite all my anxiety the party went well. Yes, I screwed up on a couple of the invitations, and there were some people there that mom hadn't even talked to in 20 years, and I should have called her dear friends in New York rather than just send an invitation because it didn't arrive in time for them to get a flight, but everybody had a good time even so. Particularly my mother, which was the point of it all.
Use this program to work through your your negative thoughts. No, you can't avoid the party, but your family wouldn't have let it be held at you house if they didn't think that you could handle it. Why does your family scare you? Are they people you wouldn't be friends with, given the choice? If you are scared because you don't want to disappoint, go through a Thought Record to see if you can bring some perspective to that.
Personally, I see nothing wrong with the hugs and young cousin strategy. I've used it quite successfully in the past myself -- people rarely question the fact that you are keeping their children entertained and quiet.
Do you know something else that I'm noticing (because I'm paying more attention to it)? Lots of people don't remember the details of all their friends and family members lives. Of course we compare ourselves to the few people who have verbatim memories -- I knew a woman who kept written notes on every person she met, right down to what they took in their coffee. Sure, she delighted everyone she spoke with because they felt valued, etc, but I found it a little creepy.
One tip I've found helpful sometimes is to, in the days before the party, look in the newspapers, etc, and select 2 or 3 topics of conversation that you can pull out if there's a lull.
It probably would have helped me if I'd done some peaceful stress relieving exercises before my mother's party, rather than have a clash with my pre-teen daughter about appropriate attire for a family birthday party not being mini-skirt, bare legs and strappy high heels, especially in January in Canada!
Hope this helps a bit. Good luck -- you'll be fine :)