Your 1 or 2 years old should be easy enough to move since they probably don't have the root mass to be much of a problem.
Your older herbaceous peonies will be a much larger challenge. If I had it to do, I would probably look for natural points of division and try to take 1/3 to 1/2 out with a sharp spade - and just leave the rest in place (or optionally put the remainder in other bags - depends on time and room, I guess).
For the record, I have, on multiple occasions, cut a piece of a peony root off without disturbing the rest of the plant. Most people that will share don't really want to dig up the entire bush. It has always worked, but it has also always been fall. They always still had stems up, too, which makes it pretty easy to do.
I've got no experience with or opinions about tree peonies.
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