I think you need to take your time coming to a decision, but I also think you need to challenge your thinking now that the initial shock has worn off.
This isn't any failing of yours that you 'didn't manage to keep your DH interested' and not all men will be unfaithful. Selfish men who are in the habit of lying to their partners, will though. I think it would be much more productive if you recalled examples of selfishness and self-absorption in your earlier relationship and concluded that this is just another example of it.
As you post more, it's clear that it's not just you whose feelings he has trampled on, to get what he wants. He also betrayed the only male friend he seems to have nearby.
Rather than admit the truth to you about why he had left your bed and wasn't in love with you, he garnered sympathy from you about his depressive illness. You don't say much about what he is actually doing about his own behaviour now, but I predict that he will be wallowing in his own misery to an extent and appearing to be on the verge of a breakdown. If so, this is just more self-absorption and avoidance from dealing with his own core selfishness. It might look to you like genuine sorrow and contrition, but it's not. It's sorrow for the mess that is now his life, not yours or your DCs.
I think you also need to step out of what looks like a protector role. If you haven't told OW's DH what has been happening and you won't tell the people in your life what you're dealing with, you are shielding your husband from the consequences of his actions, which further enables his failure to take responsibility.
Regarding your options, it seems the only one you're realistically willing to pursue is one where you try to forgive. The sham marriage one is not realistic because you still have feelings for him and this would hamper your recovery and ability to make a new life without him. It's also a bad model of a relationship for children.
There is a middle way, where you make some stringent conditions about what change is expected on his part - and as suggested by others, where you carve out your own life independent of him while you watch what he does to save his marriage. This can be a slower process because all the while he's still there and no-one knows what's happened, the shock and motivational properties of loss aren't truly felt. If you decide on this option, you've got to find a way of convincing him that he might still lose you - and mean it.