The card text states:

Dominance: Put Lady Stonehart into play from your dead pile.[...]

Is the following interpretation correct:

If playing with multiple copies of Lady Stoneheart, e.g. two, and i would have two on the table, technically one as a duplicate, and the duplicate is killed and in the dead pile, i could not put it out because i have still Lady Stoneheart "in play"? I would have to loose both copies and then both copies could resurrect simultaneously, so i would have again two copies at my disposal?

Duplicates go to the discard pile, not the dead pile.

As mentioned, duplicates go to the discard pile, not the dead pile, so you would not be able to use the ability.

As for the larger question of resurrecting unique characters from the dead pile directly into play, there is an FAQ entry on the topic. Page 10, I believe.