I'm not sure why it has fallen to you to resolve this situation. I realize you know the family well, but honestly, do you really think there's anything you can say that will make a difference? There are a zillion reasons why Janet is becoming more and more belligerent - she hates lesbians, she feels people blame her (as the mother) for Julie's sexual orientation, she feels Julie would still be straight if not for Jenna, she's a drama queen, she's experiencing mental illness or dementia and losing her grip, and a whole bunch more.
For 10 years, she's been treating Jenna badly. She continues to get a ton of attention like this, because everyone's focusing on her and trying to defuse the situation. So she's the center of attention. Kind of like kids who prefer negative attention to no attention at all, Janet is acting out in order to be the center of attention. And everyone is giving in.
Janet has to be allowed to stay home from family events. She doesn't like the definition of "family", and even if Jenna were not family, she'd still be on the guest list. So Janet wants to control Jane and Julie's guest lists? That's not how it happens.
The answer to Janet's threats should be, "Okay, we'll miss you. Have a nice day at home." End the conversation, hang up the phone, change the subject, help clear the plates, anything. Take away her power.
She chooses to stay away from her grandson's birthday party. If she were there, she'd be dominating the conversation about how she can't believe that horrible Jenna is there, so it's better that Janet stays home. Jane's son has to get used to what everyone else has to get used to - that Janet is intolerant, has anger issues, is depressed or anxious, whatever. He doesn't have to know - he just has to know that Grandma has issues sometimes or doesn't feel well. (And he's 16 - he's not an idiot, he can see what's going on.) So what the son needs is a chance to have a great party surrounded by people who love him enough to get along. If Grandma doesn't want to be a part of that, that's her choice. But the day is about the kid, not her. If she can't see that, I cannot imagine what you could possibly say after 10 years that would make a difference.
The only choice here is for Janet to miss the birthday party, and Halloween and Thanksgiving and Christmas and Chanukah and whatever the family celebrates. Jane and Julie can continue to send her a birthday card or a Christmas gift, a note about the kid's report card, whatever - just as so many adults send letters and photos to grandparents who live far away. They keep the notes short and peppy and full of family joy, how much fun they have, etc. They can keep inviting her or not - although in the short run, I would say NOT. Just stop the drama. Don't inform Janet of events - she doesn't want to come if Jenna is there, and Jenna is coming, period. Jenna is not stopping Janet. Janet is stopping Janet.
I think you should ALL just say to Janet, when she says she's not coming, "Okay, I know how you feel. We'll miss you." And stop there. Just what you do with a toddler having a tantrum - they go to their room to rage in private, but you don' grant their demands. You take away your attention from them, and eventually they figure out their behavior is unacceptable. If they don't figure it out, then at least the day isn't ruined for everyone else.
Jane, Julie and Jenna need to learn that we don't need to go to every fight we're invited to. And if you continue to discuss this with Janet, I think you will probably continue to fuel her rages. I know you want to help. I am quite sure that you cannot.