They tend to start fights over parenting issues.
They want to influence their partner's behavior and the way they treat their kids!!
BIG NO NO!
It doesn't work!!!
Why? Because he is in charge of that.
Instead of criticizing or challenging him when you see something he could do differently, give him positive feed back when you see stuff he does right:
"Hey! I really liked the way you talked to your son yesterday! Spot on"
"You have such a refreshing connection with them... Nice to watch."
Etc.
Do that a lot!
It's super validating and energizing when your partner recognizes your parenting skills.