That's weird. "We insist you all come over here and eat nothing but ham and ham and ham and maybe some water, but don't forget we also have ham!"
I'd just RSVP that my family (whoever lives in my household: spouse, kids, etc.) wouldn't be attending. If asked for a reason, I'd say directly but pleasantly, "We're going to eat more than just ham for that meal. Have fun without us!" And respond to any insisting with, "I'm afraid that won't be possible. We're going to eat more than just ham for that meal." I like Margo's idea of RSVPing like this in an email so all the other family members can see it, and adding something about how others are welcome to join you.
If one family does it, then others will likely not feel as bad if they want to follow suit. And frankly, it's such a weird thing to do, that I don't think it's rude to explain why if asked. Helpful, possibly, since they are unknowingly being poor hosts. Not wanting guests to bring extra dishes is a host's right, but being offended when someone merely politely offers help for a large family meal? That actually is rude, I think.