(I've never done this, but this is what I've read.)
Others surely will post, and either add to my post or correct a few things.
From what I understand, you can most definately add the swarm to the weak hive. I think that sounds like a great idea actually. You'll have to find the queen from the swarm, and kill her. Then place the box that has the swarm in it above the weak hive. I'm guessing you have some frames of honey and brood in there with the swarm too. That's the usual way people get the swarm to stay in the box.
Anyway, put the swarm ontop of the weak hive, seperated with a couple sheets of newspaper that has a few slices in it. Not big enough for the bees to crawl through, just big enough for the scent of the weak hive to come through. The new swarm and old hive will chew through the paper and integrate.