Minecraft! There’s lots of modpacks as well that give it variance and replayability
Especially now with the expansion of “datapacks”. I hate to say it, but Bedrock version of Minecraft might be the way to go. Java would be fine too, but unless they’re a bit more technical it can be harder to get multiplayer going for mods.
I did this previously by using MultiMC (now PrismLauncher). Make a mix of mods, send them the zip of the whole game instance and ask them to drag and drop it onto MultiMC. The biggest issue I encountered was one family member having a black ingame world until they changed a setting in the graphics mod, otherwise it didn’t seem to be too hard.
By comparison Minetest is much easier for playing mods with family. Everyone downloads the server’s mods when they join. But the interest is lower.
Terrarria has 2d shooting, cartoon violence that is kid friendly, and you can have up to 8 players in a world.
Palworld, rent a dedicated server, anyone can hop in or out as necessary. Guns, legally(?) distinct from pokemon monsters to catch. Cartoon violence. Tons of fun to be had.
Not FPS, but Valheim is plenty fun. Also, zomboid, but that ones a bit more violent
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.
A survival game is probably what you’re aiming for here. Someone has to host in those scenarios usually unless one of you pays for a dedicated server. I don’t have a ton of experience with the shooty kind. But Valheim, Vrising and Palworld were a lot of fun for about 20 to 30 hours each. Palworld had some shooter experiences.
I like these because it usually turns into a “let’s get things done together “ and everyone finds their tasks to do. Then you put it all together and you end up with a cool base you built together and have some pride in. Palworld again is the one with the lowest “violence” imo
