From what I know and have been taught, your peonies are planted too deep.

As far as dividing, do it in the fall, get as much of the root ball as possible, divide that so each division has 4-6 'eye's', and replant in a prepared hole with plenty of compost/manure/soil mixed in well.

Mine are in full sun facing south and my fushia colored one bloomed like crazy this year. This was a division from the one that had been planted in our back yard over 50 years ago and my DH accidentally mowed over. It took about three years before it 'woke' up and bloomed.
Here is last years pic of it. This year, it had twice as many blooms and was about 6 inches taller. I always deadhead after blooming time and then in the fall, I cut back the whole plant to about 5 - 6". I have never fertilized and never water it. I will be dividing it this fall. I have other areas I want to try it in.
Sure do love that yellow one. Wow! What a beauty. Want to trade divisions? Let me know.

Ok. A & D Peonies says that you shouldn't cut off the blooms! It will actually cause the plant to not do as well. That sounds backwards from other plants, but they are the experts. Also, not too deep. Ants just love the sweet secretions, they are not needed for the plant to bloom properly. Just a myth.

Here is something else I just thought of. If there was a peony planted in that spot before, she needs to remove all the soil from the area and replace it with fresh. Peonies and roses release a chemical into the soil to inhibit the growth of competing peonies and roses! Cool, huh?