What you need is an XOR circuit.
An XOR circuit allows either switch to change the state of the door (open/closed). This means the door can be opened or closed using either switch and it doesn't matter if the other switch is up or down.
I have done this but it can be tedious trying to get the Redstone to laid out correctly. In the diagram in the link A would represent a switch on one side of the door and B would represent a the switch on the other side.
There is none
There is a big stonking problem with the double-extender. It doesn't work vertically. At least not, if you want multiple of them after one another.
In order to line up the pistons, only one side may be used to power blocks adjacent to the pistons. So, let's look at what our redstone has to do when, and where it can do it.
For a down-pushing double-extender to work, we need to take a look at the following schematic:
In order to "close the gate", we need to extend the upper piston first, by powering the top block:
Then, we extend the lower piston, by powering the bottom block:
With this, the double-extender is fully extended. Now we need to pull it back in. For that, we first retract the lower piston by powering down the bottom block:
Now, retract the upper piston by powering down the top block:
Ooops! Now we have a floating block.
To fix that, we need to extend and retract the lower piston again, by powering the middle block:
Good, now we have the theory down.
In practice, this cannot be done on just one side (which is the requirement for having multiple of them in a line). It is impossible to power all three layers individually at these distinct times, because redstone takes up a vertical air block.
A condensed one-sided Double Extender only works horizontally (as taken from Minecraftwiki.net:
Vertical double-extenders only work with powering from multiple sides. For that purpose, I have also built an upside-down version of this vertical double-extender (again) from Minecraftwiki.net:
Best Answer
You have to note 3 things: