I just wanted to say the advice above is given because of experience. The intent is to watch out for you.
I have heard and believe that if you are in a relationship so quickly that when you break up it is worse than your divorce - can you imagine that pain?
As far as kids 6 months to a year from dating your partner is recommended assuming you are divorced. This is for the kids healing or adjusting.
Personally I am wary of people who have not been divorced for at least a year. Either they are in too quickly or people need time to reset. There are exceptions but few.
Gently if he is dating you and you are still legally married what does that say about him and things are moving quick? Whst does that say about him? Don't you want someone who values marriage?
That being said these are based upon experiences of wise people. TIME is the best indicator. Slow Down if he is meant to be he will be.
Work on establishing on a new family with your kids. I can't imagine what that would say to your kids because you are still married. They don't understand the difference between you involved legally married and the affair while he is married. Give them time and to add on that extra bit of knowledge is difficult - the divorce will be hard enough.
Good luck but seriously no matter how great this guy is or if you are the happiest couple he will be there for the future if he is a good person worthy of you. Take time - it will give you time to heal and you will see him not with potentially wounded eyes but as he is. I hope it works out because to find love again is a gift but honestly the experiences of those based upon what you wrote it is most likely too fast but there are exceptions. Be smart!