I am not a lawyer, but I have been divorced with children.
So far as I know, you can just file papers as to you having custody, and your soon to be ex can have visitation, and that's the end of it. Wow, wouldn't THAT be interesting!
Your friend can file she wants her soon to be ex the moon, stars, and the planet Mars, but has she actually gone to court with him?
And I will tell you something else that is certainly just a personal opinion. This 'not being comfortable with dad' is more than likely something mom is involved with. I know it's your friend, but I saw it not just in my divorce, but numerous others.
"Gosh, dad is now living in a bad neighborhood. Dad is not very responsible. All dad cares about is work. Are you children afraid to have dad take you off to school?"
And so it goes.
MY opinion. You've done enough already. Hopefully nothing comes of it. But this is a divorce. You don't want to be hit and injured in their cross file. It's likely to get worse before it gets better.
Good luck, and hopefully, dad was just ranting on the phone, because he was angry. I DO NOT blame him one SINGLE bit. He is the dad. Mom decided whatever she felt like, and dad is left sucking wind.
If I were dad, I'd have her mom in court so fast her head would be spinning, and I would spare no cost to make sure it happened yesterday or the day before.