I've just made another hotel, but when I click on "Redesign exterior", it always brings me to the exterior of the first hotel...
Or is there at least a way how to delete a hotel and build it anew?

Not sure, have not tried that yet....but same happens if I click it too. Did you try to complete it, to see which hotel actually got changed?

I tried, and only the first hotel changes :(

Not sure sure what (if anything) can be done then, for one that was already created.

Probably best try make sure you have it the way you want, when making a new one...at least until it gets figured out.

Could be a bug or more likely the games' just not fully coded for dealing with multi-hotels yet....much like so far being unable to build in * marked cities.

Actually when you are signing up for a new hotel, there is the color wheel and you can change the exterior for free then, I figured it out before I made my second hotel,
The first one is the standard one, the second one I changed when I signed up for it.