In PvP it is important to know the enemy and to have a good overview to be able to react to their actions. By watching your vids I had the impression that you lose a lot of time targeting the enemies.
In 2v2 you have only 2 opponents which makes it easier to watch their actions. I would recommend you to start using Focus target. You set one enemy to your focus target and target the other that you try to kill.
Having a focus target allows you to quickly CC it. For this you can use focus macros, which will cast whatever spell you want to the focus target without losing your current target. To start with, I would create a macro for you CC abilities with the following line:
replace Fear with whatever CC you want to be able to cast on the focus target.
/cast [target=focus] Fear
It is a nice way to get fast CCs. You DON'T want every spell to be castable on the focus target, you would need too many key bindings for that. Usually CCs are enough, this includes counter spell (Spell Lock). You should be capable of interrupting for instance the healers cast, for this you don't have time to switch to the target and use your spell lock.
You will see very soon that it is extremely nice to watch casters, because you see whenever they cast something, but it also helps on melee targets to fear them.
Another possibility would be to use arena1 or arena2 macros, but for the beginning you should stick to the focus target.
EDIT: You have to set the focus target with /focus or by right clicking on the arena frame, in your case gladius if you didn't change this option in the config of gladius.