The rooms did have a common exterior wall with which we could take measurements off of. The trick was that there was an opening between the two rooms where things needed to line up nicely. The floors would be installed in the same direction in both rooms, and when they came to that opening, they should line up.
Adjoining Rooms
As it turned out, we would have to start laying in the hallway that was in the dining room. Normally, try to install on the longest wall first. That did not work out in this situation. In either case though, you need to establish a common point between the two rooms and have a line to go off of.
Getting a Reference Line
I measured the living room in both of these locations and found the room to be only slightly out (1/2 ") of square. I split the difference and marked each end of the room. I then had John hold a chaulk line on one end of the room away from the kitchen. Then I went into the kitchen and pulled the line tight. I had another one of my little helpers watch the line as it hovered over the mark at the other end of the dining room. This was about the middle of the string. When it was dead on, I placed the string on the floor and had him push the string onto the floor in the middle. John and I then snapped each half of our line. This gave me a place to measure off of in the kitchen and insured that I would be straight and lined up with the dining room.
Another thing to mention is that these marks should be set as multiples of whatever the plank width is. For example, our planks were 3 "wide, so the mark was something like 96" from the end of the hallway. That line represented where a course of planking should come to. John and I then decided that because of the way the kitchen was laid out (see the diagram) it was going to be very hard to measure off of the line and guarantee that we would be perfectly straight so I asked the customer if it would be OK to place a plank perpendicular to the planks in the other two rooms. We would put it right in the threshold of the door. This still kept a great look and solved our problem. Even if we were of slightly, it would not be noticed. Later I almost regretted doing this because we ended up being dead on. Taking the chance was not worth it though.