The best family games like Yoshi's Island are Yoshi's Woolly World, Super Mario World and Kirby's Adventure. Below are 9, 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 Yoshi's Island 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.
The best of the modern entries, and the craft look is gorgeous.
The game it is a sequel to, and the best-designed 2D Mario.
The other Nintendo platformer built to be kind.
The other one that rewrites the genre's rules entirely.
The most polished 2D platformer since.
The SNES platformer with the best secret design.
The modern 2D Mario, and the closest in playfulness.
If the handmade art style was the reason.
3D platforming built to be generous and full of small inventions.
Edge. Family games rarely go anywhere uncomfortable, and a few of them are too generous to hold an experienced player for long alone.
The full list is on games like Yoshi's Island — 9 picks, no genre filter.
Yoshi's Woolly World. The best of the modern entries, and the craft look is gorgeous.
No. Yoshi's Island released on the Super Nintendo, 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 Yoshi's Island 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.