Where does one administer the iPhone to tell it of the two choices?
...the Slingbox Directory. That's where they always are on regular, web and mobile SlingPlayer versions.
If the iPhones and the Slingboxes are all inside the home network-- and you don't see them/can't add them in the Directory-- post back with any other details you've noticed and we'll take it from there.
It took me a bit to get into edit our two accounts, but I did get into the Directory editing place and got both Solos into both of our accounts (one had the two already).
Now I have noticed (for the first time) a Directory tab on the iPhone, if you manage to get to the right place. The directory on both of our iPhones now has both Solos listed.
Summary for others:
Administer your directory information (correctly) on your Sling Account.
Then find that menu that offers a Directory choice on your iPhone. Hint: Disconnect first.