The best family games like Aladdin are The Lion King, Castle of Illusion and DuckTales. Below are 6, 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 Aladdin 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.
Same era, same approach to animation, and considerably harder.
The Genesis Disney platformer that got the controls right first.
The NES Disney platformer everyone still names, and the pogo stick is why.
Two-player Disney platforming built for a child and an adult together.
The Genesis platformer to compare everything else on the system against.
The modern version of this idea, and the animation is still the point.
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 Aladdin that are not family games, so they are not on this page:
The full list is on games like Aladdin — 10 picks, no genre filter.
The Lion King. Same era, same approach to animation, and considerably harder.
No. Aladdin released on the Sega Genesis, 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 Aladdin 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.