What priorities would a good, family loving father have? What things would he be against?
You can write different type of fathers.
The one who love but can't said his feelings properly or see this as being weak: You write it distant, with small talk, but when the kids have a problem he suddenly pop out of nowhere to help them.
The loving one who show it: You write it by having lot of talk with the kids, cudle often with them, kiss them, overprotective (even more if he have a girl), you can even write him jealous if the kids tend to be more with the mother than him.
The hatefull father who secretly love his kids: For some reason he show that he hate his kids, can be various factor depending of the stories, but secretly, he either protect them or wait for the good time to take actions for them.
The "I'm going take the milk" father: It's the easiest one to write! Just write a small line with him saying I'm going to take the milk, and never write about it ever again.
The real hatefull father: This one depend the stories too, it can be a father who curse or bully a lot his wife/kids, be it physically or with words. The extend of the curse/bully can grow and even reaching killing/killing attempt.
This just some archetype that you can deepen by giving them some emotions, role to play, goal in the life, etc...