The Bigamist, directed by Ida Lupino, 1952

Edmund O'Brien turning on the charm.

They put some thought into it. You can see how the guy ended up as a bigamist.

You know how, on sit-coms, when a couple is trying to adopt, they try to really suck up to the person from the adoption agency? Edmund O'Brien was sort of the opposite in this. He and his wife, Joan Fontaine, go to an adoption agency. He's a bit surly. He's hesitates slightly when asked to sign the form allowing them to investigate every aspect of their personal lives, but he does it. The investigator, Edmund Gwenn, finds him living in an apartment in Los Angeles with his other wife and baby.

This happens early on and it says right in the opening credits, "Edmund O'Brien as THE BIGAMIST" so I'm not giving too much away.

The story is told in flashback. Even the adoption agency guy is understanding.

He's a traveling salesman. He's away from home five days a week and he gets lonely. Out of boredom, he takes a ride on a tour bus to see the homes of the Hollywood stars. He tries to talk to a Ida Lupino, but she's just as surly as he is. They begin dating. He tries to end it and he doesn't see her for a few weeks, but when he sees her again, she's having some terrible health problem and he impulsively proposes. Then he finds that his first wife's father just died, so he couldn't very well divorce her then. And his fiance was sick so he couldn't upset her. 

It's a little slow like movies of that era tend to be. Even if he weren't a bigamist, Edmund O'Brien doesn't seem like someone who should adopt, although he was helping out a lot with his baby in his second marriage.