Here's a quick list of inexpensive games I think your kids could enjoy. All of these are shared screen games and I've played (almost) all of these with my kid who is around the same age. All of these run great on my Steam Deck.

• BattleBlock Theater $15 on Steam
• Broforce $15 on Steam
• Castle Crashers $15 on Steam
• Cuphead $20 on Steam
• Duck Game $13 on Steam
• Earth Defense Force 5 $60 on Steam (currently on sale for $15, ends Sept 1)
• Earth Defense Force: World Brothers $40 on Steam (currently on sale for $10, ends Sept 1)
• Just Shapes and Beats $20 on Steam (currently on sale for $12, ends Sept 7)
• Left 4 Dead 2 $10 on Steam
• Lovers in a Dangerous Spacetime $15 on Steam
• Overcooked $17 on Steam
• Portal $10 on Steam
• Rabbit and Steel $15 on Steam
• Screencheat $15 on Steam
• Stardew Valley $15 on Steam
• Unrailed $20 on Steam
• Wizard of Legend $16 on Steam

All costs are in USD, so they should all fall below the 20 EUR mark.

Of these games, I would absolutely grab EDF 5 while it's on sale. It's just plain, stupid, fun and at $15 it's a steal. Saw EDF World Brothers is on sale as well, though I haven't played that one, it looks like it's the same dumb fun as the others.