Welcome to the forum!
I can't explain why the Inkscape window doesn't get larger on the smaller screen. I'm not sure if it's possible for a computer to use one resolution on one screen and another resolution on another screen. Maybe, I really don't know. Do you know if the screens use 2 different resolutions (resolution, not size)? Do other programs look different on your 2 screens?
I've heard that with the next major version release, Inkscape will work on the high resolution screens. I'm not sure if it's built into the development version yet. If so, you could just install that version. Hopefully someone else will post before too long.