I don't think there is a single tool that can do what you are describing. A good place to start would be Create point features along a line—ArcGIS Pro | Documentation.
This will allow you to create the points every 700 meters along your line, but it would not exclude any points. For that you would have to use spatial analysis comparing your new points to your two existing point layers....selecting out just the new points you want and discarding the rest. Then use the resulting points to split your lines.
The only other method I can think of is writing a custom script (python probably) that would do everything you describe above.
I guess it depends on if how often you are going to run this analysis. If you are going to run it many times, or you'll want to change up the distance between points, etc. I would write the script. If it is just a one time analysis I would try the first method.