I think Carolyn's crushes on Roger and on Burke were partly from the fact that she wanted a daddy figure, and also because they were new and out of the ordinary for her. It's easy to forget, but Roger and David were only recent installations at Collinwood when the show began.
Carolyn is supposed to be this slightly wild girl. Elizabeth is pushing her and Joe together as hard as she can and it's Carolyn who doesn't want that kind of permanence--and as much as she feels for Joe--he's too steady and too nice for her tastes. There aren't going to be any surprises with Joe.
Burke doesn't take any of her nonsense. He's good-looking and he's rich. He's got the whole mysterious past thing going on. And then there's the fact that everyone gets apoplectic when she starts getting involved with him. To top it all off, he's not related to her the way Roger is. What more could a 17-18 year-old girl want?