Should a husband be patient with his newly-reverted Muslim wife who intermingles with non-mahram men and goes to mixed swimming pools, or should he divorce her?

A person may embrace Islam without faith fully settling in their heart. The faith of some recent converts has not yet taken root in their hearts, and they need time to increase in faith and openness to Islam through gentle argumentation and goodly preaching. Therefore, the husband must be patient with his recently converted wife—as long as she is chaste—and strive to guide her, gently dissuade her from what was mentioned in the question, teach her about her religion, and seek help from righteous people. However, if he finds her to be unfaithful, he is not permitted to keep her.