The fight is only triggered once you complete their loyalty missions. You need a very high Paragon score to defuse it, but not nearly as high for a Renegade solution. If you side against one you'll need a full Paragon bar to regain their loyalty. If you're a full Renegade you probably won't have a problem with keeping them loyal. If a Paragon, put off their Loyalty missions until later in the game. Finish other recruitment and loyalty missions plus morality-based side quests before completing their loyalty missions. This will allow you to level up your passive class talent to maximize Paragon/Renegade scores and fill up your Paragon bar.
It's actually a percentage. It's how many points you have divided by how many you could've gotten up to that point. If you import from ME1, you start out with a bonus which allows you to do any charm/intimidate for the first half of the game. Jack and Miranda are easier to intimidate, while Tali and Legion are easier to charm. It is generally advised to do Jack and Miranda's missions as soon as possible; that way, the deviations from paragon and renegade don't accumulate and your import bonuses have a greater impact.
I'm not sure about the Renagade side, but on the Paragon side, the last segment needs to be at least half filled to choose the Paragon option.
An alternate way is to side with one of them. The one you side with remains loyal, and the other loses her loyalty. Then later you can regain that loyalty if your Paragon/Renegade scores have picked up to the sufficient level. The only problem with this method is that when you lose someone's loyalty, you permanently lose the option to romance them, even if they are your current romantic interest. You can only regain their loyalty, not their affection. RS Kossery 06:41, November 2, 2011 (UTC)
The best way is to wait until you have either full paragon or renegade to do their loyalty missions so you can keep both of their loyalties, failing that you can side with one of them, wait until paragon or renegade bars are full and then regain their loyalty.
The most effective method i've discovered so far is to hoard as much paragon or renegade points as you can (go to all the hub worlds, charm/intim all the vendors, do as many of the side quests as you can (give Aria the datapad from archangel, save Daniel, do Zaeed's loyalty, etc...), and talk to everyone on the Normandy (as well as Joker and Kelly after each mission as they may have new dialogue which can give you more points) before finishing the last recruitment mission of the 1st batch of dossiers. When you've gotten as much as you can do the last dossier, followed by Horizon. Then go to Illium and repeat the charm/intim all the vendors, and then do Miranda and Jack's loyalty missions immediatly (Miranda's should be available just after Horizon and Jacks just after you do Miranda's), as was stated before you will get the Paragon/Renegade options to keep both loyal because it's not how much you have at that time it's how much you could have compared to how much you have. Each mission offers a chance to get more paragon and renegade points which adds to the side of the points you could have which is compared to how many you do have (think of it as a fraction: Points you have/Points you could have), to get these options you need to have a specific percentage (no idea what they are though).