Thanks for the upload! I watched it super early in the morning today (after having been up all night) so I might post a little now and then when I watch it again give you a little bit more...
This, by the way, is where I'm coming from: I'm a masters ranked (random partner) 2v2 Terran. I generally don't play the style you saw in the replay, but when I do the absolute scariest thing when I go for my timing is to see that my opponents have a healthy (greater than 3) number of sentries which are backed up by stalker zealot. The reason for this is that my army (especially if it's marauder heavy) army is extremely weak if I can't kite, if I get split up and if guardian shields go up.
I have to say, if you guys had survived that initial push I think you would have had one scary army out. I liked that communication and planning on your part.
Keeping that in mind, some of the biggest opportunities I saw in your replay were: building placement, tech path decision making, scouting, and army composition.
So, building placement. This one is pretty straight forward, whenever I play I'm always delighted to see buildings built at the top of a ramp. Not only does this give me an easy scout of exactly what you're doing, but it allows me to exploit the range of my units to pick off structures regardless of your army size. It also lets me feel safer going up a ramp because I know that there can't be as good of an arc at the top waiting to blast me to little bits. If you had your buildings away from the ramp not only would it have allowed you to maybe better deal with his army (we'll get to your composition), but also give you a few more seconds for your tech structures to actually produce enough scary units to fend off the attack.
Next, tech path decision making. I have to admit, colossi terrify me as a Terran. Like actually every time I see a colossus I want to curl up into a little ball and die, but very early colossi without a good gateway ball to back it up turns out to be pretty useless. I liked the communication you and your ally had, but I thought the decision for both of you to tech really hard, really fast was a little too optimistic. Generally speaking, when I'm playing 2v2 either myself or my partner will tech (lets say I 1-1-1) and the other will get a good core of basic units and defense (bunkers, cannons etc.) to protect me until my cloak banshees strike fear into the hearts of my enemies. Coordinating with your ally, and picking a build that will let at least one of you get a good defense is critical, especially because most 2v2 maps have such close spawns allowing for earlier timings before your tech pops.
Another very big opportunity for your team was scouting. You had two chances to scout and see what was up that got missed. The first is your basic early scout, before a marine pops you can troll around the base and take note of things like gasses and barrack/supply depot count. In this case a scout of their base would have revealed both having gas and one adding on a tech reactor and another barrack before you would've had to get out of there. Since reapers are all but useless TvP you could assume that at least one of them was going for some marauder heavy aggression. The other missed scouting opportunity was that observer that sat on the outside edge of the base for a full minute. Unless you are playing some pretty gosu terrans they're not going to see the cloak distortion, and it would be pretty rare to see a turret up at that point. If you had gone through the base at 6:30 when the observer got to their base you would've seen everything and maybe been able to prepare a little bit better. At the very elast, if you leave that observer at the entrance to their base you can see when they're moving out, giving you time to prepare.
The last thing I noticed this morning was your army composition. Now, I already mentioned coordinating so that only one of you is going for really fast tech, but what do you do once you've made that decision? Well, like I mentioned, sentries are really scary, so the non-teching player (because you'll have gas) should be getting sentries and stalkers, while the teching player should have enough extra minerals to pump out zealots. with the composition staged at the top of your ramp you can use forcefields and guardian shield to great effect to slow if not send back the attacking army. If one of you had had 4 or 5 gateways and warpgate tech researched by the time those stalkers engaged in mid map you most likely could have had gotten enough sentries out to hold them off until a colossi or immortal popped (and just for this particular replay, once you scouted that tech lab on the rax it probably would have made sense for the teching player to pump out immortals rather than colossi).
So, I don't know whether this all makes sense (again I'm super sleep deprived but for some reason am still up) but please let me know if you think I'm crazy, have other questions/feedback or want me to look at another replay.