There may be an external source of interference that is causing this noise to get into your amp.
There are a number of possible causes for such interference.
Anything that plugs into the wall is suspect.
Anything in your house that runs on electricity is suspect. Even battery powered devices.
You need to begin a systematic approach to determining where the noise comes from.
I have the Rumble 200. I use my iPad with the auxiliary input.
I have no noise issues with this arrangement.
The only time I notice noise related to the aux input is if I have the cable plugged into the aux in, but not plugged into my iPad or anything else on the other end.
One of the issues with these cables, is that the shield may have nowhere near full coverage.
The poorer the shielding, the more likely it will let in noise.
My experience with these 1/8th inch, aux in, type connectors is that they are, as a class of connector, one of the worse designs to be found. Just because they are the smaller brother of the 1/4" plug, the smaller size, in my opinion contributes greatly to its poor performance. I find that I have to go through many different iterations of this type if connector before I find something satisfactory. If you find you have to force these or hold them a certain way to make them work, you may also be damaging the Jack as well. One thing I look for on these connectors is that there is a substantial seperation between the tip, ring and sleeves. I've had these connectors from what I consider the best connector manufacturers and have found some of them to be junk. It just seems to be a crapshoot with these things.
I think that trying just two cables is not enough to conclusively remove the aux cable from suspicion. YMMV.
Your description of trouble plugging in this connector, reminded me of all the trouble I've had, over the years with these. The problem was so rampant that I advised my co-workers to avoid 1/8" connectors whenever possible.