In order to show panels / "taskbar"s on multiple monitors when using Ubuntu MATE / MATE desktop environment, I've always used the instructions in this Ubuntu MATE thread:
Multi monitors panel layouts and background switcher
What happens if you remove a monitor:
- the panel / "taskbar" that was / were intended for the removed monitor will be shown on one of the other monitors, in addition - you may remove them
What happens if you re-add the monitor removed before:
- the panel / "taskbar" intended for the removed and now, again, available monitor will be shown on this monitor (if you did not explicitly removed these additional panel / "taskbar" before)
N.B. I'm currently using this setup with a Linux Mint (standard at the company I work for) but with MATE desktop and 2 monitors. I use the "Redmond" layout (fits my needs, don't like the "traditional" 2 panel layout).
Keep in mind:
- if you want the app buttons to be shown on the additional "taskbar" you have to (re-)add them on the new "taskbar" (panel)
- you may add some / all of the "tray" icons to the additional "taskbar" according to your needs (look for "indicator" when adding them)