Despite all the negatives you're facing from the beavers, I'm sure learning to trap them and getting to the point of finally catching some was a great bonding experience for you and your son.
Typical beaver colony is the adult pair, this year's offspring and last years offspring. In rare cases where some of the 2nd year offspring will hold over for one more year, but usually those leave sometime during that second summer and find their own area to start a colony. That leaves you with a typical colony of something like 4-8 beavers, so hopefully the one you saw was just a holdover from the previous family and you nearly have them eradicated. Do you, by chance, recall the size of the beavers you caught and the one you saw?
