I love my peonies. The blooms don't last very long a week to two weeks is probably the max you can expect. Many bloom types will shatter due to rain or wind which is why they need to be planted somewhere they are protected. Mine are under a maple
tree and like it just fine there.
It's very true about the planting depth needing to be as close to 1 inch as you can manage. Which is also why mulching them is not recommended. I've also ran across information that recommends alfalfa pellets as a good food for them. So I scratch it into the soil around the drip line for them. They are the same pellets you find in rabbit food although I did buy mine at a on-line garden center.
Understand that peonies don't like to be disturbed, so if you move them you may have to wait 3 to 8 years for them to bloom again depending on the variety.
I would definitely move the trumpet vine. Peonies last from 75 to 125 years and some types run into the 100.00 of dollars to buy so I wouldn't risk loosing them to an invasive vine.