It doesn't seem, from the OP, that Jane was upset at the mention of Joe, though? Rather that she was upset that OP had told her DH the whole sordid story.. which isn't the case but OP didn't get a chance to explain that before Jane got upset.
I'm going against the crowd here, I don't think it was rude for you to have sent the text. I totally would have texted my BFF if I saw her nutty ex in the mall. Unless of course, I knew that he was someone whose name she never wanted to hear again, but it doesn't sound like that is the case.
I think using DH's phone to send the text gave her the impression that you'd told DH everything about their past, which would be a little weird but husbands and wives do share things, and I don't consider it gossip. But I think it would help if you told Jane, "All that I shared with DH is that you two used to date and that he was a jerk to you."