They aren't easy to divide in the spring, sorry. Best time is in the fall when they die back and go dormant. If you'll still be in that house in September-November it'd be better to wait so you don't kill the plant, especially if they have a lot of growth on them already.

No, we are moving in the next month. :(

I'd talk to the neighbor who originally gifted them to the previous owner of your house, she might be willing to divide her plant again in the fall. That might be the only legal way to do it, anyway--I know here at least it's illegal to remove plants from a rental yard without the homeowner's permission.

It wouldn't hurt to try!

I know if one of my neighbors admired my peonies I'd offer a piece of root in the fall, I've done it several times.