Pikuniku has a coop mode (that I didn’t try).
The mischievous Untitled Goose Game has one too.
In the Ibb & Obb coop puzzle-platformer department, there’s also Shiftlings.
Children of Morta is a simple dungeon crawler/hack’n’slash where you fight hundreds of skeletons and goblins, but the storytelling (all voice-narrated) and tone of it were pretty much designed to emphasize a reassuring ‘wholesome family’ vibe that you may find suitable for kids. Perhaps too difficult (it has boss fights) but at least it comes with difficulty settings.
If you’re not particularly looking for coop, check out the recently released Calico and Kasi.
Calico is a colourful collect-the-pets adventure game. There are cats and puppies and capybaras and racoons and foxes and mini-horses and, and pigeons with hats!, and you can ride them all, and there are magic potions… It’s sort of a modern, everything-friendly, everything-positive, everything-inclusive Strawberry Shortcake, and it’s great fun.
Kasi is a gardening/plant designing game. Very simple mechanics, highly intuitive, and compared to other plant sims out there (where your plant grows while you’re offline, think Viridi), this one is more about assembling a vegetal bricktower through a single sitting. Grow roots for water, leaves for sunlight, flowers and fruits. Few tools but admirable for the variety of plants of different shapes you can come up with. Minimum is maximum here, it’s a little marvel, really. John Walker reviewed it on Buried Treasure, if you’re interested.
For more information, they all have a Steam page.