Dove Through the Comics
Dawn Granger, whether she's acting as human or superhero, transforms quite a bit throughout the 5-issue miniseries and the 28-issue main series:
In the Beginning
When Dawn Granger first assumes the Dove role, she is assured of herself, but not quite sold on the idea of working with a loose cannon like Hank, especially when he transforms into Hawk and seems to forget himself completely. Hank is still swathed in grief for his brother and is using fighting to drown out his feelings, and so Dawn ends up having to save his butt more often than not. For her, it's like being saddled with a kid brother she neither wanted nor needed. But she's also astute enough to see that Hank needs her help, otherwise he's going to end up getting himself killed.
Starting to Work Together
As they work together, however, she learns that in fact she needs his brute strength sometimes, because finesse, evasion, confusion, deflection, and redirection will not solve everything they come up against. She can rely on Hawk just as he relies on her--in fact, she finds out that she works best alongside Hawk, and she becomes comfortable doing that most of the time. Thus, Dawn realizes that she doesn't always have to have the solution to everyone's problems, which is a load off her mind.
Druspa Tau and New Powers
During Issues 14-17, Dove comes much closer to the source of her powers (Terataya, the Lord of Order), in the mystical dimension called Druspa Tau. As a result, her abilities evolve, taking on more of a magical tint. Now, when she becomes Dove, there's an even stronger serenity and certainty about her, which lingers on even after she goes back to being human after the danger is past. This certainty, however, begins to irk Hank just a weeeee bit. LOL
The Partnership Breaks Down
Toward the end of the main series, however, we see Dawn becoming a little tired of having to clean up Hank's messes. She doesn't want to drop him, because she knows he's still fragile emotionally (no matter how tough he acts!), but their ideologies begin to clash more and more often, until their cooperation begins to feel like a pissing contest. Dawn is tired of fighting, as their enemies ramp up seemingly stronger and stronger and Hank seems drawn into that chaotic violence. In ways, she knows she can never return to her previous way of life, pre-super powers, but she wants to find a way to have a balance back in her life, too.
Overall
In general, we see Dove becoming stronger in her own powers, but also learning that there are some problems she just can't think herself out of; she has to approach them more directly. And, much to her consternation, she finds out there are some opponents you just can't maneuver into thinking the way you want/need them to, either (ahem, Hank). Like Don does in death, Dawn learns to pick her battles, and in doing so gains a lot of peace of mind.