Father wants primary custody

Tell dad to hire a Tough family court attorney, go to family court, seek sole custody, use the fact that mom is unfit and then after he gets custody, have him file for support from Mom. THen push the divorce. If she is pressured sufficiently she should come around to realizing that holding up a legit divorce is not in either her or her kids best interest.
Your friend should work not to kick her out of the kids lives no matter how unfit. If the court gets the impression this is an attempt to cut her off (based on your question with him having a 90/10 split of the time that may be why mom wants joint custody) it will give the kids to her or even think about foster care. He better work at making her a better mom.

I can't believe I am saying this but, take a good look at the way Kevin Federline (K-Fed) handled his children with Britney Spears. It was the right medicine at the correct dose.

Good luck to your friend and his family.