I think i have a solution!
I'll try to explain...

1)Create Obj1 and Obj2
2)Obj1 is for the rotation in fig 1; it will rotate in one direction only.

3)Obj2 is for the secondary rotation, obj2 rotates in TWO directions at once.
4)Obj2 has to be connected to obj1, so that obj2 rotates in concert wtih obj1. But at the same time keeps its own local rotational axis.

I found a way to do this.

5) rotate Obj1 BACK a little.
6) parent Obj2 to Obj1
7) rotate obj1 (and thus the parented obj2) back to its original position.

now...
8) Start rotating Obj1 as you wish.
9) Pick Obj2 and rotate it around its local axis.

10) Rotate Obj1 some more...
11) Rotate Obj2 some more...

This should work, I tried it myself. hehe if I understood you correctly.