And his ex "wins"... Right? Isn't that what she wanted--to drive you two apart, mess-up your relationship, break apart your family, be the most influencial parent. You're headed into a custody battle and you're talking about kicking him out of the house-?! That's not the stable loving united front you want to portray when you're about to fight for custody.
Did he cheat recently? I know you've just found out about it, so you're processing it as if it is new information. But, you already knew there was something unfulfilled with him to seek something with the ex-girlfriend. I mean, you've already worked through it, right? It's just more painful and upsetting because of who it was with--and you don't like her! So your pissed (and understandably). But it sounds like his cheating with his ex happened the same time as with the other woman... To me, whatever factors rationalized (in his mind) or influenced his cheating with one woman also influenced his cheating with the other. On a certain level, it's water under the bridge--because you've already dealt with why he cheated seven yrs ago.
I'm not saying you shouldn't be angry. You have every reason to feel hurt. But keep in mind that, unless you think he is the same man that he was 7 years ago, keep your perspective. Focus on your priorities. Recognize that his ex probably did it to get leverage and probably was a little jealous of you. What's the old saying: Don't throw the baby out with the bath water. You're about to fight for your step-daughter. You need to be a united team.
There's nothing wrong with telling him, "I loathe the man you were when we married. The more I find out about the things you did, the more shocked I am that we married. It's a good thing you're not the same person--but it's going to take me a little while to work through this. Because it may have happened years ago, but I just found out about it. It's "new" to me! I am so angry that I'm tempted to make you leave the house for a while, but I know that your ex is hoping I'll do just that. And as pissed as I am, I will not let her manipulate me with my marriage and our family."