It may take awhile to dredge every such story I've read up from the depths of my mind but got one that does not quite fit but is close enough I'm putting it in "The Magic Meadow" Alexander Key (author of witch mountain and the forgotten door).
Just one book and sadly out of print. Its a wish fulfillment story that starts with a bunch of long term resident kids in a hospital that is about to be closed. They are about to be sent to different hospitals and they all dream about this special place where they can walk and be outside then one of them manages to go there and suddenly he can move a little. Somehow they can go to this place and it gradually heals them but may contain danger...time is running out before the closure so they prove it to some of their immediate staff and hatch an escape plan....then explore the new world. The story does kinda explain where (and when) they are toward the end, a future preserve, but doesn't really explain why it provides magic healing or how they were able to wish really hard and get there.
Midnighters is another maybe. - Kids born at midnight can enter a secret hour where everyone else is frozen and the monsters come out to play and they get a usually double-edged power and rarely fit in well with other kids because they aren't quite of this world. You do know what the world is but the rest is weakly explained though containing internal logic
The Dark is Rising Series - Is another maybe 5 kids in various combinations go into other times, weird waking dream states, and deal with myths come to life. Some books fit better then others but 5 kids are featured, there is magic, the other realm stuff is less common in the books with the drew children and more common in those featuring will stanton and bran.
The neverending story (book - peter s. beagle)
There was a recent series (yes I occasionally still read YA along with many other books) about an entire world for children who become ghosts...possible movie coming...I'm blanking on the name and author...three books
Plenty of YA material in dragon riders of Pern (Anne McCaffery founded the series her harper hall series (sub series of pern books) is YA some of the more recent work was written or co-written with her son Todd...she died recently) they start from earth and go to a world with teleporting and time traveling dragons which they engineered with lost tech from a native life form its complicated....only some of the books are YA. The author insisted it was science fiction, some called it fantasy...I use science fantasy.
While talking about young people in magical other realms you may wish to check out the work of Mercedes Lackey, some of her books qualify there...can't think of any 100% qualifies though.
Segev mentioned Xanth and I would also consider one of the books from the apprentice adept series Flach & Nepe become quite active late in the series along with some of the others of the next generation and are children.
If you want characters that start in another world this list gets way longer...lol?
Do you want stories that contain teens or young adults?
I will sleep on it...i know there are more exact matches out there.