I just wanted to give you a great big hug. I have been where you are. The DDay from hell, with the WS who has the history yours has, with the failed polygraph and the horrific reaction he gave when he failed it. Never saw any of it coming.
I think the main difference in my sitch is that he'd been in intense therapy for SA for a year, and the poly was actually required by his IC and not me, which is common in SA recovery therapy led by a CSAT IC. The reason being that active SAs, and those early in recovery, are often lying sacks of shit. The polygraph determines very quickly if there is serious work going on or if smoke is being blown. I am in agreement that he failed it, and that polys early in SA recovery are only useful in telling the BS what they cannot see for themselves at that time. He's not going to pass it any time soon, not until he fully realizes how broken he is, how pervasive the lying is in all aspects of his life, and he has done considerable work on himself in a therapy.
The other difference in my sitch is that I and the IC talked extensively with the polygrapher beforehand, so he had the back history and inside info to develop the right questions. The polygrapher had years and years of experience with SAs and with sexual predators. So there was no doubting his expertise. But honestly from what you've told me, your polygrapher sounds legit. It is more common to pass when you are lying than the other way around, and both are rare.
In addition, when we were given the results, both his IC and my IC was there with us. That way, they could both see his reaction, and prevent a lot of the gaslighting, blameshifting, honestly straight up emotional abuse that often happens when a cheater is freshly caught with proof. And the BS has the chance to get away from the WS if there is danger or if s/he just doesn't want them around. I am sure you are still getting a lot of this shit from him now. Ignore it best you can.
Now is the time to focus on you. Get you a top notch IC with experience in trauma, and with spouses of SAs if you can. Get you a L and get educated on all your options. Get yourself to the doctor and get tested for every STD available, and some anxiety and sleep meds. Engage in the full 180 and figure out what you need to do to feel safe and be happy again. If it means kicking him out, do it. If it means calling in the family and friends to support you during this time, do it. If it means up and leaving him with the kids on an extended trip anywhere for a while until you figure stuff out, do it.
I agree this is a gift. You now know what you are dealing with. If he is really worth staying with, he will own his shit and go through recovery and fix himself, without you. You have no effect on that, it is out of your hands. What is in your control is taking care of you and your kids, and doing what is in your and their best interests. The rest will sort itself out.
I am so sorry this is your reality. I know it's hard, and it sucks beyond belief. But keep posting, and we will get you through it.