Extra piece of information:
now I shut down the Personal Hotspot, bringing back the iPhone to the "suspected" wi-fi network and the photostream on the iPhone immediately showed the pics I took on the iPad (but not those I took on the iPhone, which are present in the Camera roll, but not on the Photostream). Those pics showed up on the Mac already earlier, thru the Personal Hotspot connection on the iPhone
So it seems that this wi-fi network allows for very good download to the iOS6 devices but for some reasons does not allow the upload to the photostream of the new pics from the iOS6 devices.
On the other hand, if the added pictures is on the Mac, then it is uploaded and immediately shows up on the iPad and iPhone.
To make things even more complex, my girlfriend has iphone 4S and iPad 2 both on iOS6, and for her the photostream works perfect with this wi-fi network... really bizarre.
I consider the issue closed: this network does not like me for some reason, I'll be back to my normal network tomorrow and things will be (hopefully) back to normal.
Thank you again.