Since you've only had the JRT for 9 days, they probably haven't quite sorted it out amongst themselves yet.
I have one dog that is very posessive over toys, and they are both posessive over me. Linkin is much more laid back than Coal though, so he tends to get "pushed around" a bit more and doesn't seem to be bothered too much by it.
I implimented NILIF before I even got Linkin, so naturally when I got him it went on to be applied to both dogs, Coal being the more dominant so he gets fed first and what not.
In my experience, I haven't seen much proof in the doorways thing, I've seen it mostly for rewards (food, toys, affection etc.). The thing I find most important when it comes to doorways is that *I* go through first. This has nothing to do with dominance, but rather because I have two large dogs and if they get into the habit of bolting through doorways someone's bound to get hurt (most likely me or another family member).
Coal and Linkin still squabble over toys every now and then, but I always watch their play. They love to play tug and this stupid "I'm guna bite your face" game (they lay on the floor and grumble and growl and chew on eachothers faces, it's quite halarious to watch). Once the noise and intensity escilades in their play, I step and tell them that's enough. Coal's the one who usually listens first and so if they both don't listen (Linkin is young and gets wound up very easily) I will catch Linkin and hold him with his front feet above the ground until he stops squirming. I tell him "settle") and put him back on the floor. If he doesn't try to run and play again I give him praise and tell him "good settle". Usually though, just me stepping in and saying "settle down" or "knock it off" then they will quit, though this is from learning what this means for the past couple of years.
Some toys I keep out of their reach unless I pull it out specifically for them to play with or as a good reward. I've found certain toys they squabble over more than others.
When it comes to trying to get affection from me, my number one rule is if *I* didn't want to pet you stop nudging and bothering me! They both must sit first before being pet. I've never had squabbles about my affection though, mostly rude nudging and butting the other one out of the way.
I'd suggest implimenting NILIF and watching the dogs to see who has the more dominant personality to determine which one should be fed first etc, but until you know for sure just make a guess at it.
Also, one on one time is very important. I even go as far as to do "special days" with my guys, where one gets to go out with me and do something (be it go to the school to play in the park, go for a long walk, go up town to run erands etc.). Usually (though not always) the next time the other dog goes with me. One on one training is very important too. I spend more time training one dog at a time than two, but I do do two of them at once as well so that they can learn to listen even if the other one is there too.
I hope this is helpful, though I have to apologize as I just woke up and have barely had one cup of coffee so I'm not quite fully awake yet!