The short answer is no, there is no built in tool or configuration that will automatically activate selections across all joins and relates on every layer and table that has a relationship to a selection in a master feature class.
It could be custom programmed using arcpy.mapping functions, but the complexity of the program would depend on how flexible or inflexible the set up and behavior needs to be. If all of the field names that the joins and relates are based on are identical in all feature classes/tables that makes it much simpler than if there are several field names involved. Also, if all of the joins and relates are set up in advance and will not change that is simpler to program than a dynamic configuration that needs to detect when things are added or removed from the relationship tree at runtime.
Anyway, much more information would be needed to get a program set up, but it sounds like this would be an add-in button and/or toolbar to deal with the user interaction.
Frequently what starts out as a static set up ends up having to be converted to a dynamic set up once a user gets a taste of what programming can do. At that point there is often a disconnect between the user's belief that new behaviors should be simple to add, as compared to the programmer's realization that each new dynamic option adds new levels of complexity to the program's ability to anticipate the user's behavior and the interactions between options.