Peonies are known to be covered in ants, but the ants have nothing to do with the flowers opening. Cut the buds off the plant just before they open up and before the ants have a chance to attack and they will open indoors.
Ants are attracted to peonies because the flower buds produce a sweet liquid that the ants use for food. The ants will not harm the flowers, but you do not want to bring them into the house either.
Peonies need full sun, except in the hottest areas where they can take partial shade. The rhizomes need to be planted at the right depth. Keep the soil dry to moist but well drained. Proper care will go a long way to helping the peonies bloom in the spring.
Peonies will not bloom for a variety of reasons. Peonies may not bloom until they are three years old. They will not bloom if they do not get enough sun, if the soil is not fertilized, if they are planted deeper than 2 inches, if the soil is too wet or if they are attacked by fungal diseases.