First, the word "role" does not appear anywhere in the Bible. However, instructions to submit, which sometimes are directed towards wives, can also apply to husbands.
"Submit to one another out of reverence for Christ." Eph.5:21
So, God does want us to be aware of the needs of others, and sometimes, that means submitting to a wife's decision, particularly if it is in the realm of her decision making, such as cooking, meals, etc. And a man that is active in those areas, well, God bless him!
As far as child rearing, I do believe having a father who is strong on the discipline side, (with love!) is so important to the kids. The father needs to set boundaries and limits and be willing to enforce them. So that means discipline, including time outs, losing privileges, and the occasional corporal punishment, if the other things don't work, and the law allows it where you are.
Our motives as parents is not to set out arbitrary rules for each other, but to remember how Christ would have acted, and how our actions will bring those children to Christ.
Small children, contrary to popular opinion, do need to be trained up in the way they will go. If you establish external limits when children are small, in love, they will learn to internalize those boundaries. As they get older, they will need less and less disciple, as they become self disciplined or self controlled.
The world says let kids raise themselves. And when they get old enough to understand, then start disciplining them. Except, by then it is too late. That is why this permissive attitude has resulted in such a messed up bunch of teens, doing drugs, on-line bullying, and an epidemic of suicides.
Sorry, got caught up on biblical child rearing there. I hope you will be a strong father, and intervene, but also, listen to the ideas and suggestions of your wife.