Does the father not contribute to the support of this child at all? That is what matters. Not wanting to contribute to college costs is not a factor.
This sounds like the father doesn’t plan to contribute to college costs.
The key thing is…does the mother contribute the most in terms of supporting this student? Not just for college…but now? If yes, then the mother is the custodial parent.
But as noted, a lot of Profile schools require the financials from the non-custodial parent as well. And it doesn’t matter how long ago the parents divorced.