I think you need to rethink your mapping systems. They are not showing what you think they do. Those points are not in alignment in real life.
The problem comes with the use of the draw function on Google Earth. It's not drawing straight lines on the earth.
Google Earth "wraps" their map around a rough globe shape. Whether a map is laid out flat or wrapped on a globe really makes a big difference. These difference are all about the way the map is projected onto the globe.
Lets start with one of the maps that have been posted to this and other threads. I don't remember who posted this particular map but it doesn't matter for the purpose of illustration of the problem.
See how the northern adjacent borders of California, Nevada and Idaho are curved? You can see the same curve with the northern borders of Arizona, New Mexico and Oklahoma.
The northern borders of those states are all exactly east/west with no curve in real life. To display them wrapped on a globe they have to be curved to fit. Even more telling of the distortion in direction is the northern border of the United States which is due east/west in real life but in google earth world it's been turned into a series of angled lines.
Using Google Earth to draw straight lines from one location to another does not allow for a true course. To display a straight line (rhumb) on a globe the straight line will always appear curved. If the line you draw isn't curved then it does not represent a true bearing course.
Interestingly Google Earth does use modified geodetic rhumb line modeling for their measurement function so if you are measuring due east west the measurement will be very accurate and for other bearings the error increases to about 14% depending on the bearing.
Drawing bearings is not supported in Google Earth. A straight line drawn on a google map will not represent a constant bearing in the real world.
In other words what appears to be intersections between your drawn lines don't exist. They are strictly an artifact of the Google Earth drawing function. In real life these locations are not intersected by a constant bearing between two points.
Here is a Utube explanation. Unfortunately it appears only British and Indian natives can explain this on Utube. I chose the Indian Utube because the instructor is speaking English which I can understand. The revelations about rhumb lines and curved lines being straight is towards the end.
Google Earth can not do what you are trying to accomplish. You will need to upgrade your mapping tools and understand the limitations of the mapping system and projection you choose. I would suggest the
QGIS program if you want to get serious about investigating these spatial relationships. QGIS is free and can accomplish anything any other mapping system can but there is a learning curve. In my experience precise quality tools always have a learning curve.