Was it Snow Patrol that sang about a sincere apology that didn't mean they didn't enjoy it at the time?
He's sorry. Truly sorry. He enjoyed it. So he's lying to try and scrape some get out clause out of it. He was weak, disrespectful to you. Forgiveable perhaps. What would make me think less than anything of him is the old 'I was just going with the flow' - I'd more readily forgive my DH for a private dance he admitted to enjoying and was sorry about than for being a sheep.
It wouldn't be a marriage breaker, and the house you live in is both of yours, and really to involve his mother is rather dangerous ground... it invites opinions that aren't purely yours and your DH's. However, if it were my DH with the same lame excuses, we would not be sharing a bed for a while, even if it meant I slept on the sofa not him. But I'm a believer in taking myself out of a situation rather than ordering another into one, our bed is ours, if I don't want to sleep with DH, I will leave the room!
He needs to know you find this unacceptable. He needs to know you are hurt. He needs to understand that he needs to be stronger (either by simply refusing and not being a sheep, or lying about his enjoyment of it) because he's married, and regardless of anything else, legally he's VOWED to be exclusive, so everything else aside his actions are serious.
I still wouldn' leave him though. But it's a tough call, because my DH isn't remotely interest in strip clubs, has walked away from a night out if it looks like it's ending there (to face my wrath and being called out to pick him up) and IF he did end up paying for a private dance would at least admit he liked it, but was sorry. There'd be hell to pay for sure.
But it would be all conducted at home, in house and over a period of time... (although if it was deal breaker, he'd leave of his own accord at some point I am sure, seeing as I'd be hell to live with).
YANBU to feel very hurt and angry. Get honesty from him, judge him by how you know him (none of us can do that bit) and take it from there.