As for Henry's uncle, he may well be a dramatic invention, but Elizabeth of York (Henry's mother) had sisters, so he could be the husband of one of them, or an illegitimate son of Edward IV, Elizabeth's father. The dates don't really fit, but it's obvious there's not a lot of point expecting them to...
As for merging Margaret & Mary Tudor into one, I'm not sure how that works, given that one married the king of France & the other the king of Scotland.