V-brake seems asymmetrical I'm not a big expert, so forgive me if I use some terms wrong (especially because I'm not a native English speaker). 

I have a MTB with V-brakes. I wanted to tune the rear brake because it looked like the pad were working asymmetrically (with the right pad being closer to the wheel). What I noticed, though, is that the whole brake tends to "move" to the left, where the noodle is. If I pull the whole brake to the right with my hand then pull the lever, the right arm gets pulled while the left one stays almost in place; when I release the lever, the right arm stays in place and the left one gets away from the rim. After that, pulling and releasing the lever seems to affect only the left arm - with the right pad staying quite close to the rim, to the point that the wheel is always braking. 

In short, if I understand it correctly, the brake arms should look like a V ( \ / ) and become parallel when pulled ( | | ); instead mine look like this ( \ | ) when released. 

The bike has fourteen years and a couple of accidents on its shoulders (one affected the rear wheel, but I had it repaired at a shop, and AFAIK the rear brake was unaffected). Is this problem due to bad tuning? How could I fix it? Or should I forget about it and get a new brake?

Thanks!
Please do the following experiments:
Release the brake cable, pulling (1) apart from (2) (no tools needed). Swing the brake arms one at a time, making sure they have nice spring-y reaction the last 2-4 centimeters of their travel towards the rim.

If the movement feels &quot;rusty&quot; and the swingarms don't readily return, there is mud and rust inside the breaks. Replace them.


Now check if both push back with the approximately equal force, when at equal distances from the rim.

If one arm pushes back significantly more than the other, the coarse setting is wrong.

With the brake cable still disengaged, squeeze the brake lever a few times.

If there is any resistance, or if the cable looks rusty, it should be oiled/replaced.

When the brake arms are pressed against the rim, the brake shoe should rest fully against the rim (in contrast with only half the pad touching the rim or touching the tire). If this is not correct, the brake shoe can &quot;latch&quot; when pressed, sticking to the rim by friction.
Most probably the brakes and cables are rally old. You can disassemble those parts, wash them under pressure, let them dry and re-install them, or you can replace them with more modern parts.