Andy Naselli has some material on the Trinity and Gender debate worth checking out.
I’ve argued in some Trinity Journal articles (with Rob Shillacker) that theologians should not be invoking the Trinity in the gender debate. I agree with the idea of male headship in the home and I believe in the Son’s obedient self-distinct from the Father. However, I just don’t think that “hierarchy” in the Trinity can be translated into hierarchy in male-female relationships.
From a different perspective see Graham Cole’s presentation Trinity without Tiers.