For those who are interested in having one independent Yakuake terminal for each monitor, you can use these modifications here.

https://github.com/ngc2071/Yakuakes

Basically, they were modified to be installed in the folder /opt/.

So cmake complication would be cmake ../ -DCMAKE_INSTALL_PREFIX=/opt/Yakuake1stScreen and cmake ../ -DCMAKE_INSTALL_PREFIX=/opt/Yakuake2ndScreen

These folders are hardcoded in the cpp files. So you can look into the source code and change them to your liking. Also, just rename everything with Yakuake1stScreen/Yakuake2ndScreen (including files) for better naming, if you so wish.

I like to have independent control of each terminal. I have been using this for a long time in a very old version of Yakuake, and now I had to move to a newer Linux version. As a result, I had to figure out all the changes again, I decided to share it. Keep in mind that this is not the cleverest way of doing this, probably.