Hi Rudy,
After your right-click on your feature class that has a relationship class, and then you right-click on the geodatabase to paste the data into, you should receive a dialog similar to the following:
[ATTACH=CONFIG]17595[/ATTACH]
You can see that by copying/pasting the feature class will also copy the relationship class, the other table/feature class participating within the relationship class, and any domains.
What do you receive after you right-click > Paste?