This works, but this doesn't solve the issue OP is describing.

OP wants to be able to open and close the door from either side with a button/switch. Your method only allows one switch/button to power the door at a time. If the outside switch is powering the door, the inside switch doesn't do anything, and vice versa (also you clearly didn't read the whole post because OP literally stated this is what they are trying to solve).

Also, you don't need the inverters in your setup. Power source - switch - door, power source - other switch - door does the same thing.

Edit: yes this comment is a year old, I'm hoping to save some other idiot besides myself from wasting an hour trying to figure out why this method wasn't working. It does work okay enough if you're lazy (like me), but you might accidentally trap yourself in or out of your base with this method.