I can see OP that you are in a very difficult position, because if it is, in part, conservatism that makes your husband choose not to self-identify as gay, then that same conservatism may mean he wouldn't be happy with ménage a trois situation. You say that you know that the OM would be a deal-breaker for him, which confirms this. (Although I do think this somewhat hypocritical - he doesn't want you, but he doesn't want anyone else to have you either).
I don't know that it's realistic, though, to think that you can keep this going until your children have grown up.
For a start, at some point your husband may get the courage to act on his feelings for men. Or you may break down with the stress of it all.
The person who is in the worst situation is the OM. You have your husband & your family, your husband has his family & his gay friends, while the OM has a bit of snatched time with you. This can only be making him very unhappy. And a sensible man is not going to put up with the status quo for very long, it's unliveable.
I think you really need to examine your own childhood & ask yourself why you see this as the only template for divorce/remarriage.
Because I have friends whose step-parent was better a parent to them than their real one, who became extremely close to their step-siblings. I also have a friend who is an excellent mum to her 2 step kids & treats them exactly the same as her own daughter.
And although I can't deny that divorce is traumatic for children, your interpretation of the narrative after divorce is wholely negative. It doesn't have to be. Some remarriages & blending of families are very happy.
If you truly love your ex, then I'm sure you could make it work, and I'm sure that, even if you don't think you want to now, you could make a good step-mum to his kids. I'm sure, equally, that he could be a good stepfather to your daughters. You would both be very aware of your own experience and have the life skills to circumnavigate the problems you encountered as a child. It's odd that you talk about not wanting your children to have a dad whom they only see as an 'occasional visitor, 'not a permanent fixture who looks after them'. That does not have to be scenario here. You could have joint custody for a start.
The longer this affair goes on the more likely your husband is to find out, and that might propel you into an acrimonious divorce, when it would be possible to negotiate an amicable one, to the least disruption to your children.
I don't really believe it will be possible to keep the relationship with OM going long term, & it's not fair on him. If you lose that you could end up feeling so bitter to your husband that you are no longer able to continue in the marriage. All the more so if your husband does end up coming out at some later point (perhaps after his father has died).
You cannot protect your children forever from the fact that your relationship with their father doesn't work. That can work ok while they're small, but when they're older, no. And you will be giving them a strange model of a relationship for them to build their own relationships on.
I would try to talk to honestly with your husband about the fact that the relationship does not work for you emotionally, and that if he doesn't want to be honest about his sexuality, he does at least need to be honest about that. That would be a start.