To be romantically involved with two people at the same time; to two-time someone (cheat in a relationship).
彼は彼女と付き合いながら他の女性にも二股をかけていた。
While dating her, he was also two-timing her with other women.
あの男、二股をかけていたことがバレて別れたらしい。
I heard that guy was found out for two-timing and they broke up.
信頼を裏切る二股をかけるような行為は許されない。
Behaving by two-timing and betraying someone's trust is unacceptable.
To play both sides; to sit on the fence or try to keep two options open (not necessarily only romantic).
彼は就職先を決めずに二社に二股をかけていると言っていた。
He said he hadn't decided on a job and was keeping two offers open.
政治家が有権者の意見に二股をかけると信用を失う。
If a politician tries to play both sides of voters' opinions, they lose credibility.