Sorry, but you don’t get to dismantle the patriarchy, but keep preferential treatment to mothers in custody disputes.
Your perspective needs a lot more research to even enter the time zone where accuracy dwells. The family law system is a deeply entrenched post-feminist institution, but the outcomes in regards to custody have much more to do with how child support is structured then gender bias towards mothers.
For every dollar awarded in child support, the state is given an equal matching dollar from the federal government. This means that there’s an implicit motivation to award primary custody to one parent, despite tons of evidence and research suggesting that this isn’t good for the welfare of children.