how to Isolate Vertex Groups so they don't combine when edges collide cube A and cube B are each in their own Vertex Group and they are separated by 1 cube length.

If I move Cube A 1 cube length closer to cube B the edges combine.

Is there any way to prevent the edges of the cubes from automatically merging when they touch?
Very likely you have AutoMerge enabled in your UI. Check if this button here is clicked when you are in edit mode:



When this is on, and you move one vertex to the same location as another one (like you do in your example), the vertices are melted together. It's a feature - rarely used as far as I know - which by default is disabled.