Well, there's Tibet: A Political History by Shakabpa, which has the distinct advantage of being a detailed history of Tibet written by a native who worked in the Tibetan government. I usually recommend The Story of Tibet: Conversations with the Dalai Lama by Thomas Laird as it lays out all the major names and landmarks for those who don't know anything about Tibetan history, but it suffers from a rather large lean towards Lhasap history (as most do regardless) as well as not being written by a historian, but it is good in that gives you a good perspective on what the average Tibetan thinks regarding their history.

Otherwise, the top Tibetan history that suffers from the least amount of bias would be Tibet: A History by Sam Van Schaik. Tibetan Nation by Warren W. Smith Jr. is very good and very detailed, covering every tiny political change and detail from the rise of Tibet as an entity to the philosophical squaring of a circle in China prior to the annexation of Tibet by the Communists. He has a point to make, but he does so with an extreme amount of research and he covers a lot of ground. I actually sat down and read this book, and while I'd like to do so again, I use it mainly as a reference because it's monstrous. Even if you don't agree with his thesis, it's an excellent book to use for smaller issues like this.

There's also Holders of the White Lotus by Alexander Norman which like Story of Tibet is a bit basic, and a bit Lhasap, but it covers the main events in a little bit more detail, and while purporting to be mainly a history of the Avaloketishvara cult and tradition, also covers the political twists and turns of Tibet in a light that's a bit different from the usual story.

Most Lhasap histories will focus on the Gelugspa tradition, which is the main school of the Dalai Lama and wasn't really a thing in this time period (i.e. Tibetan medieval history) though their predecessors the Kadampa were. Most histories regarding Tibet are religious in focus and origin, but if you read between the lines, or skip over large chunks to find who the patrons were, you can find political details. Books like The History of the Sakya Tradition by Chogay Trinchan, Atisha and Tibet by Alaka Chattopadhyaya (Atisha was the founder of the Kadampa), and Buton's History of Buddhism in India and Tibet which has two translations, the first by Obermiller, the second by Stein and Zangpo. Finally, I'd point to The Yar-Lun Dynasty which is, as it says, a study of Tibet's founding dynasty, mostly focusing on the Tibetan Empire, but it follows up with the dynasty's successors and the petty kingdoms that sprang up after the empire's fall (as one son, and a bastard followed the empire's fall by laying claim to rival kingdoms).

Hope that helps!