Your experience matches the gender stereotypes I am talking about.
1) The term "weekend father" implies a parent with minimal time and little involvement with their kids. A parent with equally shared custody is not a "weekend parent"... more and more divorces end with shared custody. And, there are cases of "weekend mothers".
I am just a father.
2) "Dad's house, dad's rules. Mom's house mom's rules". This is the most logical and equal way to deal with differences in parenting styles. My daughter has always understood this, both parents are parents and both make the rules.
My ex-wife is now upset with the clothes I buy for my daughter. I mostly bring my daughter to the mall with a set budget and general guidelines (you need something for cold weather) and she is perfectly capable of choosing her own style. She picks jeans, t-shirts with sarcastic sayings, hoodies and flannel shirts. Her mom is angry with me because "her" daughter should be wearing "girl clothes".
The "dad's house (in this case dad's money) dad's rules" standard works fine... although my daughter doesn't want to wear the clothes mom buys her.
The idea that the mother sets the rules based on what she knows is best for the kids, and the dad is just a support role is rather outdated.