So glad you're going to try counseling. Persevere, and if the first one doesn't find a way to connect go check out others. You may find the kids end up feeling like one is not so horrible as some of the others if they have some to choose from.
We had two family meetings with my IC to learn how to respectfully talk to each other. S12 was sullen and withdrawn and S15 was positively rude to her, and later told me she looked like a skeleton and he hated her. I think she's wonderful, warm and smart. Go figure. Some of the things she said sank in for each of us to different degrees. I have S12 a little more comfortable with seeing a different guy because he needs help with his ADD and to succeed at school. Whatever gets them talking is good. Even if they're talking to you about how rotten the IC is, they're talking.
My IC has told me it IS possible to avoid some of the damage this all causes, if you can give them words and understanding, and model something different for them. My H is teaching my boys inflexibility and limited emotional capacity, and blow up or run away as the only ways to deal, and that when you have a marriage and kids you walk away from it (ok that's really just the bleakest most negative interpretation but stick with me), and by talking to the kids, and role playing with them, and encouraging them to be brave and talk directly to their dad they'll become aware that he has some limitations they don't necessarily have, and they may learn to forgive him and take a different route. It's muddy to me now but she assures me it's possible.
I hope your kids are able to find some comfort and understanding from another adult too.
Adinva 51, S20, S18 M24 total 6/15/11-12/1/12 From IDLY to H moving out 9/15/15-3/7/17 From negotiating SA to final D at age 50 5/8/17-now: New relationship with an old friend __ Happiness is a warm puppy.