LH hit on most of it. I wouldn't start any more talks about the R or him leaving or staying. I believe you will get your opportunity as he will eventually bring it up again. Mostly you need to listen and validate, but feel free to throw in that your preference is for him to leave if he isn't willing to recommit to the marriage.
Now, as far as him actually leaving, it will have to be voluntarily. Most jurisdictions have protections in place for spouses that mean you cannot legally throw him out. You can ask him to leave. You can make it known you'd prefer he leave, but there may be legal ramifications of trying to throw him out. I would highly suggest you speak to a lawyer. It was one of the best things I did in my situation.
As far as what your options are. Bluesea, we tell LBS all the time that it is within your power to initiate separation and/or divorce. You can decide at anytime that you no longer want to be married to a lying cheater, who is also a pretty crappy father on top of it, and make that happen yourself. IN fact, I encourage LBS with spouses that are actively engaged in PAs unabashedly to move towards that place. Just be sure you are ready to be D'd, and not do it as a way of manipulating him. This is where IC can really pay dividends because it can help you with your GAL, 180s and detachment to get you in the place where you know you will be okay being D'd.
But overall I agree with LH. Take some time. Stick to the principle of not initiating R talks. WHen he does, say what you feel you need to say ONE TIME, then listen and validate. Get a consult with a lawyer if you haven't already so you know what next steps are and what your options are. And make sure to keep your poker face if he brings up leaving again or actually does leave. Your outward attitude should be "good riddance to bad rubbish" no matter what you are feeling on the inside.
M(53), W(54),D(19) M-23, T-25 Bomb Drop - Dec.23, 2017 Ring and Piecing since March 2018