I don't know how you've kept this to yourself - well done. No point blowing your cover now, so I agree with pp to see the solicitor (which I know you are).
Not sure it's the same (with you not being married), but when I was seeking separation (not divorce) from my first H, my Sol drew up a Separation Agreement, basically detailing what I wanted (half of all assets and more money on top, to account for his huge pension versus my small one).
In your shoes, I would tell the kids myself. You cannot trust him to be honest. My first H said he would tell his family that he had cheated. I'm not sure what story he gave them, but they never spoke to me again, so make of that what you will! I'd also tell his family - afterwards though, so they can't pre-warn him of anything. Believe me, blood is thicker than water, and you may not think so now, but his family will side with him over you. I had a great relationship with my former MIL, but she sided with her cheating son when the shit hit the fan.
I think when he realises you know, and he's about to lose his family and home, he will grovel. I my experience, once he knows it's really over he will turn into an evil bastard. So please be careful.
Once you have seen the Sol and sorted the financial side of things, if I was in your shoes, I'd wait until the next "date" he has with OW. Once he had set off on his jolly, I'd tell the kids and I'd also call the OW husband. I would then text him and say :
"I know where you are and who you are with. I've known what's going on for months. I have seen a Solicitor and I have had a separation agreement drawn up, which is ready to be sent to your Solicitor once you appoint one. I've told your mother. You will need to stay with her until you find somewhere else to live. I've also told the children and none of us want you back here. I have delivered most of your clothes to your mothers house today. I have also reported you to the Police for the physical attacks made on me, on XX dates, and you should be aware, that if you try to force entry into this house, you will be arrested. I have also enlightened OW's husband as to what has been going on, and I have told him where you are right now. Not much else to say really. Goodnight"
Oh, and take copies of his wage slips for child maintenance.