Aww Lisa, please try not to fret... And like BabyBee said, no-one can tell you what to do, only you know what you can handle and what you can't.
All I will say is that A) he's a plonker who didn't cover his tracks very well at all! and B) that there is more to life than worrying about what your OH is up to.
You DO have options though sweet, so try to keep your options open and see what will suit YOU and your situation best;
* Is there any way you could have a sit down chat with him and tell him that he's now put HUGE doubts in your mind and that if things are going to work, he needs to work OVERLOAD to help out with the issues he's placed onto you?
* If you feel comfortable, how about going on a "trial separation"? This would be more for your benefit than his and you can see how you would cope going solo with parenthood - although, it does pose the problem of perhaps wondering constantly what he is doing etc.
* Suggesting to do more things as a couple. It's difficult to FORCE things,
anything in fact. A) this would get him off the net in the evening, B) you are spending more time together etc.
Sometimes in relationships you have to find the spark that made you fall in love in the first place. It can be easily lost and maybe talking to him might shed some light on why the hell he thought it'd be ok to chat like that to another woman
My motto in a relationship is do not do or say anything to anyone that you wouldn't feel happy doing or saying IN FRONT of your OH

Easy to say coming from someone who is SINGLE lol!!!
I do feel that most people stray or get doubts when there are issues they have in the relationship (some do it just for the buzz). Maybe he is feeling insecure or unloved etc?
The only way to get to the bottom of it is for you both to talk.
If all else fails, here are some necessities whilst dealing with untrustworthy men;

xx
xxx