Quoting Red Bottom:" <blockquote><b>Quoting Word:</b>" <blockquote><b>Quoting Red Bottom:</b>" ... [snip!] ... called her a "cute name". She was introduced as his sister in law, not his ex. Obviously sister in law takes precedence."
As I see where you're coming from, I can see how she's taking it and why. He left out the part that she was an ex. If he doesn't talk to her like that and is calling his ex "sweetheart" then it seems there COULD be something still there between them like a special bond or something, who knows? She should definitely talk to him about how it's making her feel (uncomfortable, not special to him..whatever it may be) instead of letting it bubble inside of her until something escalates causing more problems. But yeah, it would definitely bother me if I were in her shoes because I still have some low self esteem, then again my SO would never to do that to me because we know our relationship boundaries and I'm sure our relationships and the OP's relationship are different.
OP- It's very possible that calling her "sweetheart" means anything to him or her, but you can't be upset or mad at him if he doesn't know how you feel. If he continued to be the way towards her knowing you're uncomfortable then I would be upset/mad at that point for not respecting your feelings. Maybe you guys should go over your relationship's boundaries...I hope everything gets straightened out. Good luck mama