First off this document looks absolutely gorgeous, so that is a nice plus! Flavor wise the hospitaler seems to resemble a paladin subclass fitted into the fighter format. The hospitaler, like a paladin takes an oath giving this subclass a lot of flavor to work with. Now lets take a look at the abilities:

-Healing hands: the abilities given do not really resemble the title of this ability, you gain a lot of proficiencies that I do not really associate with the class but you do not get any healing hands like ability. Why the investigation proficiency? Also would expertise with the healers kit fit this class a lot better than the herbalist kit? I would rewrite this into allowing the hospitaler to use the healers kit as a bonus action perhaps.

-Merciful relief seems nice! Perhaps let it scale more, perhaps copy the sneak attack scaling.

-Combat medic: It is a very flavorful ability though and I can see it work very nice. The temporary hit points given are not really that high but you can use this ability an unlimited number of times, this ability seems balanced.

-Hospitalers reprieve: one thing I would change is this sentence. they can immediately make a saving throw to attempt to end one effect of their choice. (also what saving throw? Different effects require different saves. It would make more sense to choose the effect before rolling)

-Comforting respite: Spells? this class does not get spells, you sure it is not a paladin subclass?

Greetings R. Wellink