Hi there. Sorry to hear that you're hurting, and I hope your mom is ok!
If there's still time to edit your post, I would suggest going back and adding some paragraph breaks, many people have trouble reading long posts that don't have any breaks and so may not respond. This post maybe also ought to be moved to the Poly Relationships section of the boards -- more people post replies there when folks are seeking advice for specific problems, whereas the life stories section is meant to be more rambling and less feedback-focused. Just a suggestion, again to help you get more replies, the site moderators can help with that or you could just re-post this there.
Ok! All of that said, here's my take. Your husband didn't cheat. Plain and simple. You have to figure out how to get that idea out of your head. You told him that he could go for it and you picked the timing of when you did that, not him. If he has feelings for her, how is it surprising that they followed through? If he wasn't physically where you were, then it's not like he could have supported you more or been there for you more by not sleeping with her, you still would have been exactly as alone. Are you mad at him for not coming with you to the hospital in the first place? It sucks that he panicked and lied, and that he handled his responses so poorly afterwards, saying he wanted to leave, but it sounds like both of you are very jumbled up in your feelings right now.
The main problem that I see here is simply that you all moved way too fast. A lot of people make that mistake. But this is all so new, just a few months, and there's so much to sort out in terms of how you all relate to each other, what you can handle and what you're not ready for, what everyone's feelings are. Having her be practically living with you guys, having her family over to your house, all of that is just way too fast, there's no time for anyone to process and deal with their feelings rationally.
So, my advice, assuming that you want to try to make this work -- dial things back. Get everyone together -- all three of you, because she has a stake in this too -- and explain how bad you've been feeling. Don't engage in any blaming or shaming because none of you have actually done anything wrong (except for him lying, which, again, it seems like he panicked), just own your difficult feelings. Tell them that you want to be able to be ok, but that for that to happen you need some breathing room. Maybe that means that she comes over less... once or twice a week instead of every night. Maybe that means that you all set aside one evening a week where you check in, talk honestly about your feelings. Maybe what needs to happen, if she really is mostly straight, is that she and your husband develop their relationship *slowly* and you and he work on your marriage, but you and she just stay friends and not be "gfs" per se -- a three person relationship where everyone's feelings and interests aren't equal is very difficult to sustain and can build resentments, such as with you noticing she doesn't give to you in bed the way she does to him. But all of these are just ideas. The important thing is that you guys talk it out and slow down.
Like I said above, a lot of people make the mistake you guys have made, underestimating how much works it takes to get involved in poly and how slowly and carefully things may need to occur. I strongly encourage you to do some reading. www.morethantwo.com
has great resources on dealing with jealousy and on dating as a couple.
Finally, I've got to say that the part about having your teenage son report on their sexual activity seemed way out of line to me. It's not fair to put your kid in the position of spying on one parent for the other, and it must have been weird for him, listening to then have sex! Try never to put them in the middle, especially about something so personal, it's really unfair.