I apologize for not responding on the Phonescoping facebook group when you posed this question. Sometimes it is just easier to type on a keyboard instead of a phone.
Part of the reason I didn't reply is because I haven't really made any attempts to remove shakiness from a video. I typically just ditch the video if I don't find it acceptable in this area.
But, in general, I use either Photoshop Express or IMovie depending on what type of file I am tinkering with. I also use Youtube "Capture" sometimes for videos.
Hope this helps somewhat.