What is the reward for a woman who patiently endures her husband's polygamous marriage? And is she sinful if she objects?

A wife's patience with her husband marrying another woman is a great act of obedience, because the reward is commensurate with the hardship. A wife's objection to the marriage is not permissible as long as it is lawful for the husband according to Islamic law, unless there was a prior condition obliging the husband to fulfill it.