Drink a lot: not only will this help you to care less about your surroundings, but it'll also increase your range of weird emotions, which will make you fit in. You know how couples go from being smiley and happy and kissy one minute to being miserable and fighting the next? After a nice drinking binge, you can be like that, too.
Put your foot down early: They're going to ask you to leave the room at some point so that they can get intimate. The first time, you need to make it clear that you are going to watch them have sex, and unless they've got some pair or x-ray goggles you don't know about, you're not gonna be able to do that from in the hallway.
Give them a taste of their own medicine: If the above plan doesn't work and they do kick you out, here's what you've got to do: tell them at some point that they need to leave the room so you can get intimate with yourself. Nothing will shock them out of wanting to turn the hotel room into a romantic love den like knowing that you were vigorously masturbating on that bed just an hour ago.
Cry: You know how Steve's girlfriend gets whatever she wants when she cries? It'll throw them for a loop if you start crying, too. If you want to go get Italian food and they want Mexican, start welling up and sobbing. Bonus tip: when Steve asks what's wrong, just say "nothing," and then when he asks again say "you can't tell? That's the problem!"
This last tip is so expected and straightforward that I almost didn't include it: any time there is even the most minor disagreement between you and Annie or difference in opinion about plans, you need to say "Bros before hoes, dude." That'll snap both of them out of it.
Lastly, like my father always said: Push for the ménage.