I was sitting on the couch reading your post above and after reading your H's email I shot up, yelled "WHAT?!" and hauled upstairs to the computer.
If the emailed spurred anger in ME, I can only imagine what it's doing to you. I'm not a pro. Not by any stretch of the imagination.
I am a newbie and will defer to any and all vets on this, Ok?
He is an instigator. Yes, you broke a glass but let's get some perspective here: Your living arrangements are hostile at best, abusive at worst.
I, too, can be a yeller. I am reactive with my anger, also. When pushed I can hardly recognize myself with things I say in reaction to my buttons being pushed. I am not excusing my past behavior, nor am I excusing your glass-breaking and yelling, HOWEVER, given your current situation, I don't think anyone would have responded better if they'd had the tools.
Breathe. It is understandable for you to be angry. To want to throw things, break them, say horrible things. It is. However, you're an adult and there are other ways, though I'm certain you know that.
Let's get you some tools. Let's fill your tool box with assertiveness, strength, grace, less-reactivity, calm, beauty, self-assuredness, confidence and a dash of general "oh-no-you-don't, MR!"-ness.
His email is poking your wounds veiled behind false "support". Your anger and glass-breaking, as implied by him, does NOT make you a failure. Is it a good idea? No, but only because it doesn't do anything FOR YOU (and is likely not a great example for your kids).
He is manipulative and an instigator.
Here's the big question here:
Do you want to move out?
No? Ok then. Don't move out.
Get a lawyer. Like, right now, make some phone calls. I'd also advice you start documenting but not because you should have it for future court purposes but because your anger is being used against you and I think you should have something to be able to track your progress. You CAN get on top of it. I never thought it was possible but I'm doing it. My anger was a HUGE issue in my marriage and I am not proud of how i handled it at all. I now know what I need, in the moment, to do and give to myself so I don't become that big angry green monster and can respond with compassion, love and assertiveness without feeling like I've given my power away.
Of course I still need practice but I want you to know it's possible and we can chat about it anytime.
I wish I could give you more than a virtual (((hug))) because I imagine you're feeling very overwhelmed.
Ok, tell us...
what are your weekend plans? I suggest that you make some BIG ones. Something fun with the kids and something GOOD for YOU (like get to a book store and find a book that talks about reactivity in relationships). Anytime you are home, you need to be away from H. AWAY. Consider him a roommate. Cut down on your opportunity for him to berate you, speak condescendingly to you... so cut down on his ability to speak to you.
As far as an actual response to his email, I need to calm down myself first before I suggest a response. Maybe a vet will chime in while I breathe.
Hang in there, Lorelai. This is NOT easy but we're here!