Katie and I ordered two new queen bees from B. Weaver apiaries and had them sent to us via express mail, and they arrived last Thursday!
We searched through the Ambrose hive but could not find the queen, even after 20 minutes of looking, so we decided to introduce the new queen and take the risk that the Ambrose queen was still alive, which would cause them to fight to the death.
Augustine, the hive we cut out of my mom’s house, we gave brood to raise its own queen, and sure enough, they did! The new queen had already laid many eggs and there was capped brood in the comb; however, we had to kill her to introduce the new queen to the hive, so I squashed the Augustine queen, who is only a month old or so, and put in the new queen.
Why did we re-queen the hives? Well, in the case of Ambrose, the queen we had was now over a year old, and as queens age, they run out of bee sperm from their mating flights and emit less queen pheromone, which is what keeps the hive together.
This is a natural process; when the queen gets old enough, the hive either supersedes (replaces) her with a new queen they raise (offing the old queen), or they swarm, roughly half the hive leaving with the old queen to find a new home, while the other half stays in the hive and raises a new queen.
Neither of these scenarios is best for the beekeeper, usually, because you end up with a queen with unknown traits or half your hive gone, putting a big dent in honey-making. In the case of Augustine, it was a double whammy: Half the hive swarmed with the old queen and they raised their own queen of unknown genetics.
What we did know about the Augustine queen was that the bees she produced were pretty mean and aggressive, so we really wanted to re-queen this hive with a known good queen, bred for gentleness and honey-making.
We will find out this next week whether the hives accepted their new queens; sometimes they get mad at them and kill them right away. 
But hopefully they will welcome them as their new monarchs!
