Margaret Tudor & Mary, Queen of Scots

I finally got around to watching Reign and I know its very far from historically accurate but for me usually when I can place a name with a face from a movie or show its much easier for me to follow along.

I couldnt help but notice the similarities between them, after their first Husband dies. I know it was two very different situations but i guess it was similar in that their 2nd and 3rd husbands just screw them over and they had an infant son.

Did Mary REALLY still plot to take elizabeths throne? Has that ever been proven? I just cant see someone who has been through what she has been through even still thinking about that - especially after how badly you have been screwed over at every turn. Did this effect Elizabeth and James' relationship?