First, I'm very, very sorry you're in this position.
I'm not quite sure how a baptism turns into a drunken one-night-stand, but I'm not buying the story he's selling. He was dancing "intimately" with her, was "all over her" (a woman with whom he'd cheated on you prior). That suggests, to me, a continuation of the prior intimacy---not a whoops-I-drank-too-much-in-celebration-of-our-friend's-baby's-welcome-into-the-bosom-of-the-Lord "mistake."
Whatever happened, it was not a "mistake." It was a choice. If he was too drunk to actually consent to sex, then the choice was to become too drunk to remain accountable for his actions. But I'm not really buying that. It's too convenient.
Did they both cook up the so-very-drunk story because they thought it was a get-out-of-jail-free card, should they HAPPEN to get caught--something they likely thought would not happen?
I don't know what I'd do in your shoes, OTHER THAN THIS: I would not accept, for even a second, that this was a "mistake." A mistake is accidentally wearing a brown shoe with a black one, and not noticing until you get halfway to work. A mistake is forgetting to pick up the dry cleaning. Spending the evening following a baptism "all over" a woman other than your wife, "dancing intimately," and ultimately, landing in bed with her is a series of dreadful, destructive choices. Even if, at some point, the drunkenness led to blackout, there were conscious choices to betray you made. In fact, he did that the time you were home in bed and he was kissing her (and keeping that secret a delicious little thing between the two of THEM). How long has this affair really been going on? Does the other woman's husband know of the long-ago kisses? That the behavior the night of the baptism was a continuation of an inappropriate relationship?
I would take his actions as a very serious sign of an immediate need for rehab (blackout drunks are not the norm; they are indicative of a HUGE problem), and a very serious sign of the need for him to acquire some serious, grown-up boundary skills.
Because what man celebrates a baptism by getting blackout drunk, dancing suggestively with a woman other than his wife (with whom he has previously cheated), and landing (rather publicly) in her bed?
Not a healthy one. Not one who is safe to you.
You say that the issue for you isn't the infidelity per se, but whether he's told you everything. That's the case for many of us. The infidelity, we could get over. The subsequent lies, not so much. They kill marriages.
If, however, his relationship with alcohol is as strong as you describe, you may have to accept that you will never know the details. Either he was blackout drunk, or he's lying about that because he thinks it is somehow better.
It's anything but.
Whatever happened was an enormous betrayal. He wasn't a hapless victim or a defenseless puppet. He had a ONS with a woman with whom he apparently did the same thing prior. (I'd dig into that "little bit of kissing." There's likely much more to that story--and I wonder if their thing has been ongoing, with the baptism being their ...coming-out party.)
If there's more, and he knows there's more and chooses not to share, your marriage will likely not survive.
If he's an alcoholic who lands in other beds and refuses to commit to sobriety, your marriage will likely not survive.
If he got tipsy, chose to sleep with a woman with whom he's had an inappropriate relationship (harboring, at very least, secrets from you for a very long time), and decides to man up, own what he's done, and do some VERY serious, VERY hard work on himself and his relationship with you, then that's a different story. Then, your marriage may survive and even thrive.
Again, you may never have all the details. All of us have to accept that this is the case---we will never know for sure whether we do. Some of us know next to nothing. (I don't know a single thing other than what I found on my own, and much of that, my husband denied. Even three years after separation, he still refers to some very concrete truths as my "little paranoid musings.")
It's up to you what you accept. Try to remember that when things feel so very out of control.
I am so very sorry you are here, but it's a good place to be, under the circumstances.
Millions of hugs to you.