The tapestry Bard finds seems to show Thror in the same generation as Thrain... Is this a mistake, or have I miss read the tapestry?
Thorin is the son of Thrain who is the son of Thror. I cannot find a picture of the tapestry from the movie, but I did find a family tree that shows the heritage of all of the dwarves. I think you may have misread it, or that the shot in the movie had the tapestry folded slightly to make it look like Thrain was next to Thror.
Here's the actual tapestry from the Blu-ray edition: you can clearly see how Thorin, son of Thráin, son of Thrór is the nephew of Frór.
What I find rare is, however, that Thráin is not depicted directly below Thrór (no mother is shown, so it makes no sense to put it in that way. There must be reasons we ignore, of course; it would be nice to see the complete tapestry).
Weta Workshop has made the actual tapestry design available to buy from their website.
In the images provided, we can appreciate that Thráin being not directly below Thrór is just a design choice; it doesn't have any genealogical meaning. In fact, the whole tapestry has this kind of unorganised feeling we are not used to see in genealogy family trees (which tend to be very symmetrical).
I don't have a picture of the shot from the movie, but it is more likely you misread it. Here is a chart of the line of Durin.