Re: Main hive going for its third after swarm - many queens?
Welcome to Bee Source.
If I know a hive swarmed, I try to check it for queen cells as soon as I can and either use some of the cells to make splits or cull them down to three cells. Usually with only three cells there won't be after swarms.
A lot of times after swarms will have multiple virgin queens in them or the swarm will split with one or more virgin queens in each part of the swarm. I've caught swarms that had at least three virgins in them. I put a queen excluder under the hive I put the swarm in for 3-5 days, or until they are drawing comb. By then the swarm will usually stay. I remove the excluder so the virgin can take her mating flights.
There may have been one or more virgin queens in the cluster under the hive. I've had luck putting a nucleus hive close to a cluster under a hive, with drawn comb in it, getting the cluster to go into it. A frame with young brood on it might work faster but if the cluster didn't go into the box, the brood would chill fairly quickly. I don't know if leaving nurse bees on the brood would keep the swarm from going into the nuc hive or not.
"Sometimes the best action, with bees, is no action at all."