Kodit - you are in shock at the moment and so don't make any decisions at all just yet.
It might help your terrible confusion if you just had a few facts at your disposal.
Statistically, men who cheat early on in a marriage are far more likely to cheat again, whereas there is far more hope for men who cheat for the first time late on in a marriage.
What everyone is saying here is true; your H is only admitting to what you can prove. There will be far more hidden from you at the moment.
It is not possible to forgive or move on when you don't know all there is to forgive. You now need to get as much information you can from sources other than him - what have you said in your E mail to the OW?
With this particular OW, it doesn't sound like he has an emotional connection and is just bringing her out of retirement when he fancies illicit sex again. Saying he wouldn't have gone through with the hotel room is nonsense - yes he would.
Despite what others are saying, it is remarkably common for men to cheat when their wives are pregnant - and there is a reason for this. Any event that causes an under-developed character to grow up and face responsibility, produces a response like this. Marriage might have produced a similar result.
What ever you decide to do, the fault is his and not yours - and the fault is with his character.
In your shoes, I would assume he was going to be the sort of man who will be perenially unfaithful and would cut my losses now. However, I don't think you can decide anything while you know so little and while you are in shock. Therefore I'd suggest you ask him to move out while you think and find further information.