Lots of good ideas here, IMO!
If I were you, I would talk to DH about this first. If he didn't seem to understand, brushed off my concerns, continued to let her come in for that cup of coffee, then I would confront her. I wouldn't care if she denied or pulled the "poor little me" act. If one is firm enough, chances are, a woman like this will back off.
I wouldn't worry about hurting my relationship with these neighbors either. Maybe just as well. And, IMO, that's something she should have thought of!
Whatever you choose to do, please let us know what it is and how it works out. Perhaps I'm jumping the gun, but if nothing resolves the problem, maybe marriage counseling will be in order?
In fact, come to think of it, though you say you trust DH, you also are worried that if you bring this up, he'll " be alerted to the fact that she finds him attractive (he's a little vain - aren't we all) and it might escalate things." Not sure how you mean that last part. But if his vanity means more to him than your feelings - or if you think it does - maybe marriage counseling is in order, anyhow?
Good luck, no matter what route you take!