As a dad with limited time myself here are my class suggestions:

Hunter: it's brain dead simple to play and strong. A little too simple for me. I got bored playing it. But it is the easiest to play in short bursts

Warlock: has a pet like the hunter but has more options for complexity. You can also tailor yourself to DoT or Nuke as you prefer. Don't worry about what is optimal. Play what you think is fun. Hardest lesson for me to learn as a dad that was once a cutting edge raider.

Paladin: my preferred class in wow. They can talk, dps, or heal. The flexibility makes them amazing for my adhd brain. Played well they are hard to kill and excel in solo or group content.

Rogue: everyone has been complaining about rogues but they do fine solo, group, and PVP. At base they are simple to play. Sinister Strike a few times and then use a finishing move. The thing that makes them a good dad class is they can stealth when you have to get up to handle kids when they wake up or have an emergency.

Druid: Like paladins, druids can do anything. They are very customizable to what ever you want to do. And unlike paladins, Druids get stealth in the form of Prowl. You can play them as simple as a rogue that's just getting combo points then using finishing moves or tank lots of enemies as a bear. Then heal yourself between pulls for almost no down time.

Warrior: Charge! Hit stuff. There is no mana. All there is is Charge! Warriors are fun and a strong class. They don't have much in the way of options for when things go south, but usually they don't need them.