R.T.
L., wow; things just aren't easy right now, eh? Life kind of goes like that. I'm so impressed that you admitted to your part of it with the nagging and yelling and what-not, even though he is still responsible for his actions as well. Also, the forgiveness is key as well for your sanity. Are you a Christian? Both forgiveness and not nagging are Biblical spiritual principles/laws. Jesus said that He'll forgive us if we forgive, and Proverbs says that it's better to be on the far corner a roof than to live with a nagging wife. Boy do I know how hard that is, because it's not a part of our culture or nature to be a loving, respectful wife to our husbands.
With that said, I would definitely not suggest dating right now since you don't have closure. Also, if you change to do things better, it shouldn't be just for him, but because it's right and you're life will be more blessed because of it. It will also benefit your kids a lot. Whatever you allow yourself to participate in regularly with your attitude and emotions will be what they learn to do as well.
So, those are my thoughts. I have found that prayer and closeness with Jesus is the safest place to remain. The Bible says He is the King of all the kings of the earth - that gives Him a lot of authority and power to change things (and us!) on this earth, even more so when we hear His heart, learn His will, agree with Him, and pray accordingly.
Thank you for being so open and desirous to do things right. I've seen marriages like yours get totally restored and healed by God, but at the same time, you'll have to use insight about where your family and husband are at and what steps to take now. If you let him spend time with your kids, I'd highly suggest being there during those times and watching how he talks to them and what-not, not suspiciously, but just to come to grips with if his words match his actions. Again, praying for him and prayer for insight is super-helpful if you proceed along that road.
I'd like to pray for you now if you don't mind. If you're not comfortable with that you can stop reading, but I believe it will help:
Lord, I just ask you for mercy for L.. You see her heart; you've seen everything that's gone on in the back room, and you know her hurt. Nothing is a surprise to you. I ask for mercy, that you would forgive her sins and break in with peace for her. I pray that your peace would surround her and that she would have a determination to do her part in this whole situation. I pray that you would give her wisdom and insight and that you would reveal; please reveal You're heart to her - that she would be overwhelmed with you're goodness. You truly are a good God, and YOUR love for her is greater than any human love she has ever experienced on this planet. You died on the cross so that we can have full access to the One who loves us that much - thank you. And, in that, I thank you that you have felt everything that she's feeling because You experienced it too on this earth - rejection, pain, hurt, hopelessness. Thank you that you can identify with her in every way. Now, I pray that You, the "God of all comfort" would comfort her with your leadership that is good and trustworthy. We pray these things in Jesus name, Amen.