By "Family Politics" do you mean dynastic politics?

The best introduction for twelfth and thirteenth century Britain is Carpenter's The Struggle for Mastery. It's a Penguin book, so it's relatively cheap, and a great read. The bibliographic essay at the end will be able to point you in the right direction.

On a side note, I believe Game of Thrones was more inspired by the dynastic struggles of the Wars of the Roses in fifteenth century England. Either way, a good read on that period in Dan Jones' Wars of the Roses. It's more of a popular history text, but it is (for the most part) reliable enough that I've seen it used in college courses or for lecture prep.

Another place to look for introductory surveys' is the Very Short Introduction series on Britain, which is a reprint of the essays in the Oxford Illustrated History of Britain edited by Marshall.