I remember another book series (not "The Exiles Trilogy") which could fit the bill. I am not sure about the details of the story any more, but the space ship was a sort of child hospital ship named EUKALYPTUS (even though its original purpose was deep space colonization or so), so it contained lots of sick kids. The adults had, at some point, abandoned the ship - it is assumed that they assumed some catastrophic event would destroy the ship, but this didn't happen. However, the ship left into deep space. The ship was shaped like a dumbbell (two spheres connected with a cylinder), had lots of decks with sizes of several kilometers across and featuring (artificial) jungles and deserts. The ships also has an untested propulsion system which allows FTL travel (even though still "slow" considering the interstellar distances). The reasons why this ship was re-purposed as a child hospital might be of political nature.
I also remember a robot, who had some sort of attitude (compared to the usual worker robots on the ship, who acted like robots, but were disguised as teddy bears).
The single human adult on board is Daniel Locke, whom the children find in "deep sleep" in a "glass coffin" in a section of the ship normally not accessible to the children. In book #2 it is revealed that he suffers from a "dangerous sickness" which cannot be healed by Earth doctors, so they put him into deep freeze. Also in book #2, the children meet alien "space doctors" who find a cure for Locke's disease (even though it takes one of them 10 days!) and revive him.
I read the book in German and I am not sure in which languages it was available. The authors were Germans.
Authors: Hans J. Alpers / Ronald M. Hahn
Title: Raumschiff der Kinder
Here's #2 of the series (in German, ISBN 3-7709-0388-9, published in 1977): https://www.scribd.com/document/46504849/Alpers-Hans-J-Hahn-Ronald-M-Raumschiff-Der-Kinder-Band-2-Planet-Der-Raufbolde-1977
There seem to be only German language editions. Apparently, there were six books in this series:
- Das Raumschiff der Kinder, 1977
- Planet der Raufbolde, 1977
- Wrack aus der Unendlichkeit, 1977
The first three books also appeared in a collection: "Raumschiff außer Kontrolle", 1985.
- Bei den Nomaden des Weltraums, 1977
- Die rätselhafte Schwimminsel, 1978
- Ring der dreißig Welten, 1979
These three also appeared in a collection: "Weltraumvagabunden", 1986.