A shooter might be hard, but I think you could make ORION: Prelude fit. It’s a little old now, but still fun. You get to shoot dinosaurs and run around big maps.

Other games that I’d recommend: Avorion (build your own spaceships and fight and befriend the galaxy) It’s not technically a shooter, but depending on whether you pick out lasers, electric tasers, machine guns, or rail guns, there is definitely some aspects of moving to avoid enemy fire while plunking them down. [but don’t be like me and just make lots of borg cubes… because cubes are the best!]

Ark: survival evolved (tame dinosaurs and fight the map)

Elden Ring with seamless Coop mod (up to 6 players at once)

War Thunder for plane sim, World of Warships for good ship battles

Valheim is also capable of being extremely frustrating, so I’d recommend one of the mods that removes the skill penalty loss when dying. It might not be necessary, but dad knows the kids’ temperaments better than me.