It sounds as if you are turning the connection nut (long "barrel" type nut) the wrong way. The nut should "climb" up onto the upper shift rod and come off of the lower rod.
But if you are turning it the correct way and it is still not fully disengaging from the lower rod, it may be that you will need to "deflect" the upper rod a bit to get the two rods to uncouple since they could just be in a bind with one another.
I use the term deflect rather than bend to emphasize that, even though you actually are bending the upper rod, putting a permanent bend in the rod is not what you are trying to achieve. Rather, you are trying to momentarily shorten the upper rod to separate the two.
Not to worry if you do put a slight bend in the rod. You will just need to bend it back straight as best you can and use the adjustment nut to compensate for any small dimensional change that may occur.
I hope that makes sense and doesn't just confuse you more.
Good luck.