Wow! Karen, Your H is simply not to be trusted. Like Dday suggests, tell H to have his L talk to your L. And most definitely report this to your L. Your H is crazy like a fox, and he's hoping to get his way through bluster and bluff.
I cannot believe how unconscionable your H is behaving -- in public even. And pulling your D out of class just to interrogate her?!? He will stop at nothing.
On the suicide thing, given the extreme circumstances I think it highly understandable. I would say that if any LBS never, not for even a nanosecond, ever called into question their reason for living in the face of such a travesty, then perhaps they must not have really valued their M in the first place.
(Thankfully, God is there to catch us when we so fall, if we let Him.)