Do you now have a plot facing the valley or the mountain?
To be honest: you have a limited budget, so everyone has to make some compromises. If my parents built me my own apartment when I was 18, that would already be really great - but I would also accept some compromises.
Then: in such a slope, the basement is not unusual. I would say, especially with a valley-facing plot, that's the cream of the crop: direct access to the garden, far away from the street.
One option would also be to place the granny flat in the attic. If desired, its own access via an external staircase. Is a recessed floor allowed? Then the footprint upstairs can be reduced in favor of a larger terrace. Great view, absolutely private.
Then I would make the following layout:
Attic as a recessed floor, large terrace, access from outside, bathroom, living room with kitchen, bedroom, small storage room, possibly another bedroom. And the roof truss open, then you could create wonderful teen living spaces with a gallery for sleeping.
Ground floor:
Option 1: Here the private rooms, i.e. bathroom, bedroom, dressing room, children’s room (unless outsourced to the attic), no balcony or terrace necessary (no one goes from the bedroom onto the balcony - floor-to-ceiling windows with a French balcony are enough there)
Option 2: Kitchen, living room, dining room with a magnificent view. Pantry and guest toilet at the back, possibly office/guest room. Here I would also plan a balcony or another recessed floor, so that you can also get outside from the living area and then make a staircase from this terrace/balcony to the garden. (So upper floor with the smallest footprint, ground floor a little larger footprint but leaving space for a terrace, basement then full footprint)
Basement:
Option 1: Kitchen/living-dining with direct garden access, pantry at the back in the subterranean part, freezer, storage. Advantage: direct access to the garden from the living area.
Option 2: Bathroom, bedroom, possibly children’s room, dressing room, freezer and storage at the back. A sauna could be planned here as an outdoor sauna and the bathroom designed so that you have direct access to the garden. Then you can initially consider a sauna and prepare accordingly (piping etc.), think about an outdoor shower and a plunge pool or whirlpool outside (and make corresponding preparations if desired) and initially leave the whole "wellness" topic aside and return to it when finances look better again.
Both options have charm and their pros and cons. You have to decide what is more important to you.
But if the children get along well, then I would definitely plan one or two more rooms for the soon-to-be adult children in the floor that the son occupies, that will relax your space concept on the other levels.