Hmmm. I'm confused. A good lawyer will not ask for money up front when someone is in your situation. I think they are milking you big time! Usually costs are done after the divorce. In your case, since he's cheating and says he wants to be with this chick, you can ask for him to cover some costs.
Your husband cheated; that's grounds for divorce. That's pretty simple. Each child receives around 20% of his salary. If he doesn't like it, that's too bad. He made his decisions, and that's the law. 21 years is a long time, you'll get some money out of this.
One of you files, preferably you first. Take the emotions out of this, no matter how hard it is. Make sure your kids are taken care of, and yes, that they have time with their father as hard as that may be. This is not time to be an emotional wreck. You need to think business matters, and the fact that your children need to see dad and keep things as normal as can be at this point in time.
If you can't afford the house, don't keep it. If there are car payments, or he offers you the car, be careful. You may be better off asking for money rather than the car, get yourself a cheap, but safe one and use the rest for savings or other start up costs. Talk to a financial counselor so that you know what you will need long term for you and your kids.
He'll need to give you some time to get a job, find childcare etc.
Make sure you tell your children's teacher and or counselors so they can be there as support if needed.
Good luck.