What is the significance of Toy Story 3 and My Sister's Keeper towards the topic of Relationship?
If you are looking for the common thread between these two movies (stories) in the category of relationships, I think the answer you are looking for would be something that incorporates purpose and sacrifice.
In both films, the characters are either questioning their purpose in life, or seeking one. In My Sisters Keeper, Anna feels like she was only born to keep her sister alive. She turns 13 and decides she wants to stop donating, stop being tested, stop providing biological cures for her sister's cancer. She does not necessarily have another purpose in mind for herself, she simply wants to quit her old one. In Toy Story 3, the Andy has outgrown the toys and they think he is getting rid of them. They want to have maintain the purpose of being toys that bring Andy joy, but feel rejected and un-needed. In the end, they find another child who can use them - who provides them with a new sense of purpose.
This one is a bit of a strech, but certainly each movie deals with it. In Keeper, Anna has been sacrificing herself for sister her entire life. She wants to stop. In Toy Story, Woody is willing to sacrifice his safety (and position as Andy's favorite) to save the other toys.
Both films show the power of genuine friendship in relationships - but also the need for a personal sense of identity in order to make a relationship continue to grow. Both movies show that friendship isn't really enough, if both parties don't feel a sense of worth and purpose in the world.