Some thoughts.
Art, perhaps that swarm you caught nearby is actually the swarm from your primary hive which you are worried about. Meaning it has already happened. If we assume that to be the scenario then give consideration to the following supportive information and suggestions.
You were not seeing brood in the second because the queen quit laying some time ago in her preparations to leave with the swarm.
The hive is filling up with nectar-honey because when there is little brood to feed it is amazing how much they bring in and pack away! Yield goes up immensely when there is not the brood feed demand.
You caught the swarm so the original package queen is now happily setup and buzzing along in the new second hive.
The original hive is in process of requeening itself with the replacement swarm cell queen(s). There would be a virgin queen (perhaps more the one) in the hive currently asserting her reign by killing off all the others. The bearding may be an indication that there is more than one VQ - possibly staging for multicast swarms. If weather is poor that is good as chances are the VQs will escape the bees and will fight it out instead. New Queen is also hardening her body and flight muscles to preparing herself for her mating flights June 25-30.
Given a swarm/requeening situation, the action to take is to not go digging in the hive at this time. It would be best to stay out and let nature take its course while the new queen gets established. My suggestion is only to add that third box, perhaps even a fourth, directly on top to give them space to put all that unused nectar so they can clear the nest area for their new queen to get to work when she is ready.
Summary:
- hive swarmed, you caught swarm.
- main hive is getting new queen mated
- main hive needs space to put excess until there is brood to feed
... add a super, probably best add two
... check into the brood nest for eggs after June 30, assuming you are having nice weather. If poor flying weather, it may take longer. There will be little to no large larvae or capped brood. As that time will be very soon after her mating and just getting started laying. You will see mainly eggs due to the brood break caused by the swarm and requeening. Check on 3 to 5 day intervals until you are satisfied they are re-established and stable.
... have your backup plan, plan bee, ready. If no eggs/larvae by July 6, immediately order and install a new mated queen. Do not try giving brood to raise their own in this case. As by that time they will be hopelessly queenless for awhile already and on verge of becoming a laying worker situation. They will need a mated queen immediately at that time.
Imho
Hope that helps!
THP