https://itunes.apple.com/au/app/mctube-for-youtube/id652124176?mt=8
Try that, preset videos to 1080p in settings.
So does it upconvert the video, or pull only the 1080p video?
My understanding was that if you have 360P, you have 360P. Making a 1080P out of it just makes a bigger mess...
McTube will display 1080p if there's a 1080p option available for that video, otherwise it'll display the highest available quality.
the youtube app for android has an option in settings to default to HD or nonHD. i dont have an iDevice but check and see if that option exists