Unfortunately, the Slingplayer for iPad app appears to be broken. . . again. When the Roku 3600 streaming stick was released earlier this year, it did not initially work with the Slingplayer for iPad. In May 2016, Sling fixed it and it worked fine for a few months. Now, it's broken again. As you correctly noted, if you install the Slingplayer for iPhone on the iPad, it works fine and you can stream to the Roku stick. It's only the Slingplayer for iPad app that's broken. It's been broken for a few months now.
I have an interesting situation.
I have an iPad Air 2, iPad Pro and iPhone 6. All have the latest (iOS 10) software.
I also have a Roku 2 box and a Roku stick. Both devices are shown on the network with ip addresses 22.214.171.124 and 126.96.36.199 respectfully.
Now the iPads both stream successfully to the Roku box. But they do not stream to the stick. When I enter the IP address of the stick the app says that the Roku has been successfully located, but when I try to stream, there is no Roku icon does not show up in the app.
Interestingly, the sling player app for the iPhone, when installed on the iPad, works.
I have installed and reinstalled the apps on the Roku stick and the iPads, I have rebooted the router. I don't believe this is an IP address issue or the sling player app for iPhone would also not be able to recognize the Roku...furthermore, the iPad app recognizes and apparently connects to the Roku.
Any suggestions would be greatly appreciated, thank you! Kathleen