The best solution is to quit the affair and quit making excuses that he can't, and be faithful to his wife and kids.
Is he ready to get with the other woman and not see his kids every day? Is he ready to see the pain on the kids face when he has to leave them behind and go to a separate home? Is he ready to lose his soul over these actions? He is already an adulterer, a liar, who has cheated on his wife so he can't be trusted. I would not call him the responsible one if he acts like this and only thinks of himself.
Your brother took vows to be faithful to his wife and he has messed that up big time by not keeping his word. He is dishonest and he is not responsible or he wouldn't do things like this.
Even if he and his wife have different interests, they can still compromise and learn to work together as a family so the boys have a loving, stable home. They both need to be giving 100% of themselves to their marriage to make it work. He has become selfish and is only thinking of what he wants, not what is best for his kids and that is, IMHO, despicable. They are innocent and do not deserve this.
Sorry I'm so blunt but things like this just get under my skin because too many kids have had to suffer like this because one or both parents only thought of themselves. Then why do they have kids if they aren't prepared to work on their marriage and make it the best they can?
Mark 10:11
And he saith unto them, Whosoever shall put away his wife, and marry another, committeth adultery against her.
(even though he has already committed adultery, he is making worse if he divorces and remarries when he has not right to do so)
Luke 16:18
Whosoever putteth away his wife, and marrieth another, committeth adultery: and whosoever marrieth her that is put away from her husband committeth adultery.
Luke 13:5
I tell you, Nay: but, except ye repent, ye shall all likewise perish.
(which means he would have to give up OW completely with no contact of any kind or forgiveness won't be given)
Eph 5:25 & 33
25 Husbands, love your wives, just as Christ also loved the church and gave Himself for her
33 Nevertheless let each one of you in particular so love his own wife as himself