Well, without seeing your scene file I'm not sure about your setup.

But to get everything to follow the leader, so to speak, the rule of thumb to remember in Maya parenting, is:
"Children First, Parent last".

So, if you want everything to follow the position of your nucleus, or a master group node, then select everything you wish to be children, THEN select the PARENT last, and then group it


To get things to rotate, say, on the Y axis WITHOUT worrying about keyframes, you can do the following:

1. Right-click on the objects Y rotation attribute in the channel box and choose "Expressions".
2. Apply the following: yourObjectRotateY = time*80;
(Sub "yourObject" for your actual object name)

If you MUST use keyframes, then you can also open the Graph Editor for your keyframed object, select the keys in the Graph editor view, and Goto: Curves, and set the Pre and Post infinity to Cycle, and your rotation will loop