Unfortunately, relocating and releasing trapped animals REALLY messes up the wildlife in the new area of previously established animals. You may introduce disease into the population with trapped carriers. Unless there has been a die off as mentioned with the distemper, land is probably carrying the max load of various wildlife already. No place for the dumped animals unless someone gets killed fighting!
It TRULY is not kind to release animals into areas where they don’t know water or food location, have to fight with established “top dog” racoon in the territory.
We wired hard cloth wire to the cage end and sides to keep paws inside the cages, not able to reach the bait without entering. Tie or weight cages down to prevent it rolling and releasing the animal. One here reached out cage top, grabbed feed can handles to move cans, tip cage over and get out. Made quite a mess moving cans and cage, much stronger than I would have believed possible!! Took quite a while to recatch the animal, get it OUT of the barn!
Call Animal Control, the DNR, about IF you can legally relocate them and how to best move the live animals to other designated locations. Rehoming to new locations can possibly be illegal!! Perhaps these agencies will take the trapped animals from you. And sometimes the only disposal method is dispatching them. A neighbor might help you in this instance and carcasses put in feed bags for the garbage pickup. They MAY be disease carriers, I would not bury them on my property! Be really careful handling the traps to prevent getting scratched or bitten. Could be Rabies carriers inside.
If relocating, you may want to paint a tail tip, to know if it is the same animal returning. They can be very determined to come back. My friend did relocating but kept catching racoons. I suggested a bit of spray paint before release. She tried going 5 miles, 10 miles! But they still returned, had to dispatch them. They were EXTREMELY destructive, no way to “live and let live” with them. Similar wreckage to what OP is telling us.