I would like to split points (they are uniquely grouped with diff points belonging to different family of points) based on their spatial distance. One thing I don't know to get it is the distance from one point to the other and keep track of that so that when it is beyond a specified threshold, then I should break the group point and assign it to a different family of points. Kindly, if anyone could be having insights about an ideal approach, I will be more than glad. Thanks..ArcGIS Pro Python ArcGIS API for Python Calculating distance between points in a Feature layer
I would start by looking at existing tools
If your points are sequential in their ordering, then the sequential point distances aren't hard to derive. From a histogram or inspection of that data, you could decide on the spacing threshold to identify cluster breaks in the table.
This could be accomplished with cursors and arcpy, or more simply using numpy for the distance and statistical calculations.