I'm really confused how Shadowheart refuses your party (unless you are a Gith). I've played 10 games and every time you just walk up to her, say lets work together, and she joins you. ?? I guess I've never picked up Lae'zel first . . . but you really have to go out of your way to do that.
If you turn the other direction at the downed ship at the start, you can miss Shadowheart on the beach. Then you come to Lae'zel first. I suppose most people know where Shadowheart is because of the promo videos, so go to her right away.
If she refuses to join you, she goes to the Druid camp and hangs out there. So you can talk to her again and ask her to join you again. Then there are some persuasion checks that I failed. I could have save scummed, but didn't, and I presume if I had told Lae'zel to go back to the camp before speaking there wouldn't have been an issue.