Short answers, pulled from the story.
Daniel of Moscow died in 1303 without ever holding the title of grand prince of Vladimir. His son Yury inherited the small territory but lacked a legitimate claim to the throne according to traditional succession practices.
The Mongol Khan Tokhta ignored dynastic tradition when he granted Mikhail of Tver the grand princely title on the 27th of July 1304. This decision left Daniel's descendants as izgoi, or outcasts from the line of succession for the highest office.
Dmitry Donskoy passed the grand principality to his son Vasily I in his 1389 will. This act transferred succession rights from the Mongol khans directly to the Russian line and marked a clear usurpation of the traditional authority held by the Great Khans of the Golden Horde.
Before 1389, the monarch was known simply as the Prince of Moscow. Later titles expanded to include grand prince of Vladimir, Moscow and all Russia as the grand principality became a family possession of the princes of Moscow.
A decades-long war of succession known as the Great Troubles embroiled the Horde in the second half of the fourteenth century. While the Mongols fought among themselves, Muscovite princes managed to grow too powerful for external interference.