Why did Amri's supporters become stronger?
Radak: It is because he intermarried with (married his daughter to) Yehoshafat.
Why does it say "Es ha'Am"?
Radak: This is like Min ha'Am. Also "k'Tzeisi Es ha'Ir" (Shemos 9:29, is like Min ha'Ir).
Kli Yakar #1: They tricked the people with Tivni (pretended to support him), so that his supporters would share their inner thoughts.
Kli Yakar #2: Those with Amri were leaning to switch and support Tivni (but he died).
How did Tivni die?
Rashi (citing Seder Olam): When Asa married Amri's daughter to Asa's son Yehoshafat, they killed Tivni, when they saw Amri's importance.
Radak: He died naturally, and Amri became king without opposition.