I think you and your DH are fine with not going to the funeral. I think YOU should send a card from the two of you, since he does work with her, but that's as far as I would go. (I would make sure the card was in my handwriting, not DH's)
If someone decides that a card must be sent, I would have DH write it, he signs it, and writes "and", and then you write your name in your handwriting. That way she can see that he was involved AND knew that you were signing, vs you just plunking your name at the bottom. And if she just gets something in your handwriting only, she might still think that a card from him might still show up. But for him to write it and put "and" before your signature it shows that you're a team and you are fully apprised of everything.
Just to give a little background.... the family member who died was diagnosed/had surgery/began treatment years ago when DH was involved with this girl, so, while he didn't know the family member I guess he was there for her while she dealt with getting this news. The family member had gone into remission but obviously became ill again.
I hate it that I feel like this, I wish I didn't, but I think after you have been cheated on you never really lose that "what if" feeling.
The fact that he was around when the person got sick makes a bit more sense. She might feel that he would want to know.
But I don't expect regular friends to contact me about family members who have died unless I knew the family members. And I don't even expect exes to contact me. Heck, an ex had his mom AND dad died in the years since we broke up, and he didn't contact me, though I knew them, and I didn't expect to hear about it.
Maybe I am missing something. As far as I can tell, SIX years ago, before they were married, a former friend with benefits left a few drunken texts. She talked some crap about him and that seemed to be the end. Where are the stalker accusations coming from? What door is being reopened? This woman was admitedly his friend before the benefits were added. Why is it strange to let an old friend know about a death and about the funeral services? If the OP has trust issues, fine. But, it does not seem to be based on ANYTHING that happened within their marriage from this woman. Is it based on how she was with another person she dated that the OP mentioned? Come on.
It can seem like that.
But I have been on a few sides of this, and I don't think it's innocent.
I've been on the "I'll be marginally in your life while you get over the last relationship, and I do expect to be considered once you're ready" side, and it hurt worse than some actual breakups, when he skipped over me. Especially b/c in my case, the woman the guy ended up with ended up with him because she basically swooped in and "claimed" him. He later left her, and we tried to figure out a relationship again, and he told me that he wasn't sure about my feelings but he WAS sure about hers, and if he had only known my feelings he wouldn't have ended up with her... Do you know how painful that is to hear? It's horrible.
Now, I didn't act like a psycho about it. She certainly did, though, after he left her. And she was the big reason I finally ended it with him, because she'd purposely (as she went more psycho, she lost more friends, and those friends all went to him to tell him what she had plotted and planned for) gotten pregnant TWICE by him, and had had those babies, so he was linked with her forever. And whenever he and I would try to get close, she knew it, and the midnight phone calls would start. ETA: Finishing that bit....although I've been a stepdaughter three times over, I have never wanted to be a stepmom, especially not when I was already frightened of their mother. Having him in my life would mean having her in my life, and that wasn't a pretty thought. IN addition, he was considering moving from NY to WA to be with me, and I ultimately wasn't comfortable being with a man who would leave his children (that I never met, for the record) and move cross-country. It was a good decision and I'm glad I made it (though sorry I hurt him, even though he had hurt me a few times already). end of edit.
Anyway, that's neither here nor there, except to show that the situations aren't exactly the same, as I wasn't the psycho one and it doesn't seem that you are (though she might feel the same devastating pain for having been skipped over, being "not worthy", for having heard all about his divorce having been there for him etc etc).
About the calling-about-a-loss part....that probably wasn't actually done just to let him know. When I called an ex to let him know that my mom had died, it was NOT because he had been in my life when she was diagnosed. NO, it was because I wanted him over at my place, immediately. And he came over.
It was just after watching High Fidelity, which in retrospect was a big mistake to watch, because of the scene when the female character finds out that her dad has died, and then what happens when he comes to the funeral and reception at her mom's house.... That feeling of needing to feel SOMETHING ELSE, and as she basically says, "or I'll put cigarettes out on my arm", is strong and powerful, and although it's been a LONG time since their dalliance was done with, I would be that she wanted a big reaction from him.
If I were her...silence would probably be the best thing. Well, and finding someone that she can actually fall in love with and leave behind her past. Silence can't be argued with, reasoned with, persuaded. Silence helps to heal, over time. It's harder because she's at work, but there can be silence when he's not passing her in the hallways. Blocking a phone number is an idea, but just not responding is a better one.