The best family games like LittleBigPlanet are Tearaway, Yoshi's Woolly World and Super Mario Maker 2. Below are 7, each with the reason it is here — and, at the end, what filtering to family costs you.
Filtering to family means the game has to work for a child and an adult at the same table without either of them being bored. That is a much harder design problem than a difficulty slider.
What you get: Something you can put in front of anyone. The best family games make the skill gap not matter rather than pretending it is not there.
What made LittleBigPlanet worth playing in the first place is covered on the full list. This page is the family part of that answer, and only the family part.
Media Molecule again, and the papercraft world is the closest thing to LBP's handmade look.
The other great yarn-and-fabric platformer, and much kinder to newcomers.
If the level editor was the point, this is the sharpest version of that idea.
Same tactile crafted aesthetic, built for playing with someone who does not play games.
The best-feeling 2D co-op platformer of that generation, with the same four-player chaos.
Yarn, physics and a two-player rope you both hang off.
The current PlayStation mascot platformer, if you want LBP's charm with tight controls.
Edge. Family games rarely go anywhere uncomfortable, and a few of them are too generous to hold an experienced player for long alone.
Specifically, these are strong answers for LittleBigPlanet that are not family games, so they are not on this page:
The full list is on games like LittleBigPlanet — 9 picks, no genre filter.
Tearaway. Media Molecule again, and the papercraft world is the closest thing to LBP's handmade look.
No. LittleBigPlanet released on the PlayStation 3, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Age ratings cover content but not difficulty or frustration, which is what actually ruins a family session. Five minutes of unedited play footage tells you more than any rating.
With mixed ages, co-operative usually wins. The competitive ones that work are the ones where being in last place is still entertaining.
By hand. Each pick was written for the full LittleBigPlanet list first, on what the game actually does, and this page is the part of that list that is family — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the family guide for where to start in the genre generally.