When a gay man’s affair is discovered by his alibi wife who only married him to have kids, he must deal with the aftermath of their separation and battle her in court for custodial rights.

You don’t want this to be a synopsis, but a logline, so don’t give all this info. Attempt to make it more concise:

It is assumed, because you say alibi wife, that they married with her knowing he was gay, so why would she be separate? She got what she wanted (kids), he got what he wanted (covering up his sexuality).