"because they say he is always making fun of them, or correcting them, or making them feel bad. They are basically afraid of him."
You know, no...if the kids are feeling afraid of him then something should be done about it.
File for divorce? No
Suggest counseling NOW in an approachable way? Yes
We are parents first and foremost and we tend to be biased, its natural.
This is what I get from your post. You state your 9 yr/o does great and behaves in school, but you "subtly" state that he is out of control basically at home. It sounds the "fear" is coming from experiencing a different type of discipline from your husband. It needs to be redirected and done in a better manner, but I honestly cant blame him for getting onto your child for "running around/being loud" all the time. I assume "all the time" because you carefully say "very busy".
Thats ok. Who in their right mind would verbally degrade their children by saying they dont follow rules at home.
Secondly, you are VERY careful how to word things about your children, but you were VERY forward about your thoughts on his kids. Thats a problem too. You may not show your distaste of their behavior to them, but Im sure it is still obvious to his kids in other ways. So, maybe you are not as approachable to his kids, as yours arent to him. Sounds like EVERYONE needs to do some self-reflecting here and get some help if you want this family to stay together.
Maybe there is something "wrong" with him, or maybe he is getting signs from you that he and his kids are not "good enough" and are having to abide by different rules than you and your kids.
Just a thought, let us know if any of our replies have hit home and helped.
-------------------- "...And what a beautiful mess this is
It's like picking up trash in dresses..."