RangeSlider is inherited from Slider
It actually doesn't, it just contains mostly the same code.
I can not set the RangeSlider to display textures (available to Sliders)
What exactly doesn't work? Do you get an error or does is just not show the textures?
I just tried loading the black theme and using the Slider section to create the RangeSlider like below and it worked (it's not recommended to use a section of a wrong type, but it works here because they do support the same properties).
rangeSlider->setRenderer(theme.getRenderer("Slider"));
There does not seem to be a way to load textures for the space between the two thumbs.
This indeed seems to be missing.
There are 2 ways this could be implemented though. You could have a texture that has the same size as the track and of which only a part is shows (similarly to how the front image in ProgressBar works), or you could have a small texture with the same height as the track which is stretched horizontally to fill the selected area. I guess the first one would be the better option because it can handle rounded corners on the track or other special cases.