Late in act 2, Hedda tells Thea that she wants "for once in my life to have power to mould a human destiny." Does Hedda have that power? If not, why not? If so, how does she use it?

Hedda doesn't have such a power at all, because she is not even satisfied by her own life - if she could she would mould her destiny. Throughout the whole story this nasty character is trying to live through other people instead and that brings a lot of troubles to all the people surrounding her.