Tyrion's real issue is that he's knowingly trusting his family. Every mistake he made comes from trusting family or friends to do the right thing. When his family and friends are for the most part, dishonorable.
Yup. He basically came in with a force around the size of the unsullied with the 3 dragons. And before long, the entirety of the forces either bent the knee and joined or got burned and replaced with someone who would.