You are correct that it doesn't make sense. Zeke should have defected as soon as he learned that someone named "Eren Jaeger" had the Founding Titan. At that point, he should have realized that his father's mission was a success. Also, at that point ALL of the Titan shifters except the Warhammer Titan were present on Paradis Island. Zeke had Reiner, Berthold, Ymir, and Pieck under his command and could have just delivered them to the Eldians easily.
Granted, he was also unaware of the political situation, since Reiner and Berthold ran off before the coup. From his perspective the royal gover