[To be quite honest, Claire doesn't understand it much either. She's only recently come to terms with having a husband young enough to be her son. It wasn't what she was hoping for when she wished he would wake up from stasis.]

Bree, of course he would want to meet you. He knows about his children. He doesn't love you any less.

[Jamie loved her the moment he knew there was that flicker of life. It's why he had to send Claire away. Claire knows he'd make the same decision no matter what.]

... it will be strange, I'm sure, but you're still his family. His blood.