I am so sorry to hear about your situation. I have heard of this so many times and it also happened in my case... we term these people as "Overlappers". They are people who are unable to be alone so they get into another relationship -- never working on the issues and problems of the first. The pain of separation, divorce and relationship struggles can be so intense that a "new" shiny object really heals the pain. In your case and in mine, its sad that children are involved as the collateral damage. For your husband or soon to be ex-husband its unfortunate but it happens so often. They think, this relationship is different and it feels so great -- this time we will all be a happy family with the white picked fence. He is grossly lost in his BradyBunch sitcom. He has absolutely no idea... and I am sure he enjoys hurting you during the process.
First, I am sorry. You are valuable and your marriage was valuable so take time to process and learn from your mistakes. Spend a great amount of time with your children as they are going to also be an emotional roller coaster. My divorce attorney told me that after divorce each parent should not introduce another person to their children for one year. The kids need to feel stable and not fight for the attention of their parent. He said that in "all" instances of his former clients when this didn't happen the children had "mommy or daddy issues".
For your children, hold your head up and teach them -- your way. Take your time. Show them how they should be courted as they grow up or how to treat and court someone. Overlappers just don't get this process. The "happy" chemicals really cloud judgment and put a Band-Aid on a very open wound. You will need to be stable and solid for your kids. This is sooooo hard as you will need to react and be on your toes to many of the things they want to process with you on....
I will say a little prayer for you and your family. This is sooo hard and your not alone. A wonderful woman I deem my "airport angel" taught me this great notion of running a new business. "You are now in the business of raising, strong, confident, smart little girls. This is your new corporation. The corporation in the best interest of the girls." I use this everyday. When I deal with the negative and positive actions of others I think ... what is best for the corporation... This has allowed me to remove the petty crap and to think intelligently. I hope this also helps you. God bless.