I kind of figured out a workaround. This is really wierd.
I started KDE on the main computer and as it was starting up I started KDE on the remote computer but on the same display. Both started, but the taskbars did this wierd leapfrog thing until both crashed and everything messed up.
But, when I put one of the bars at the top and left the other at the bottom, both worked in harmony! I can now open local programs on the top bar and remote ones on the bottom bar. Wierd.
Also, if i xkill the top one on one screen and the bottom one on the other, I get basically what I wanted in the first place: One computer on one screen and the other on the other screen while being able to move my mouse and keyboard between the two.
I guess it makes sense: the first KDE started the startkde program and the other computer's taskbar and desktop were put on top. And, when I open something from the remote taskbar it becomes a child process and the DISPLAY setting is left the same! Sweet.