Lots of good responses here and you can see the trend. Just about any time I invite someone who's bringing a raft, they automatically get a permit spot to bring a friend. In this case you're bringing your raft and gear for his raft- and gear-deficient trip and you can't even bring a friend with another raft and gear help support the trip?
If the TL thinks it's worth turning down another raft to keep the group size under some arbitrary number he'll think twice when y'all are scraping down or missing eddies with over loaded rafts. This, of course, assumes your buddy with the raft is acceptable for a family trip and won't throw the group dynamic into a tizzy.
I concur with the overwhelming response you're getting and with cataraftgirl: at least you know up front what you're getting into (and can politely decline now if you want).
Because this truly stinks:
Sometimes you don't find out the "real scoop" until you're at the put-in with the TL's family & their gear sitting in front of your boat.
Good luck with the decision, and remember if you turn down the trip, there'll be other opportunities. Hell, you and your buddy can probably do a nice float from Grand Junction to Moab (or something comparable) with that week and have no trouble getting on someones's Westwater permit where you won't even have to play babysitter and pack mule.