One of the most effective things to do in Starcraft 2 when you're playing 2v2 is to deny expansions to the enemy while expanding yourselves. It's not that important to destroy your enemy's main - that will come at the end of the game. Instead, try to take the map and expand, while denying your enemy any expansions.
This strategies does two things - first, it gives you a bigger economy while only attacking in a hit-and-run style, then retreating. Most of the time, the defenders won't mass their army near one of the expansions, but rather at their main base. Their placement thus gives you the ability to quick-strike their expansions. All you have to do is force them to cancel or to destroy the Nexus/Command Center/Hatchery, and retreat. Don't go for the drones unless you are attacking with such a small force that you aren't going to be able to get the main building before the defenders arrive.
Better yet, do a two-prong attack. Station your main army outside their base, and send good building-killers to an expansion (anything that does high damage to armored is good), and simultaneously do a drop on one of their mineral lines. Most non-pro players will react by moving their WHOLE army to one location, which both splits their forces and allows one of your attacks to do good damage. If they DO overreact to the harass, you can use your massed army to hit their front door and destroy some buildings or defenses. After this, retreat - you will have likely lost some forces, and only the presence of your expansions (and the loss of theirs) will gradually gain you ground.