It's a Date (1940), 6+

An aspiring actress is offered the lead in a major new play, but discovers that her mother, a more seasoned performer, expects the same part. The situation is further complicated when they both become involved with the same man.
1h 43min | Comedy, Musical, Romance | 22 March 1940
Director: William A. Seiter
Stars: Deanna Durbin, Kay Francis, Walter Pidgeon, Cuddles Sakall

http://www.imdb.com/title/tt0032644/

Pleasant, yet silly, but not because they're trying to be funny. The man both KF and DD fall for is WP (b. 1897). We don't get a clear idea of how old DD (b. '21) is playing; when she was at school, I presume it was college. And WP did play the helpless stowaway pretty well, so it's not totally implausible that DD would fall for him. (WP is a year away from his first pairing with Greer Garson.)

DD sings a good bit, and KF is portrayed as having a similar voice. (Soundtracks lists Gypsy Lullaby, the opening number, as Performed by KF (all others are Sung by whoever), and lists no voice double, but I doubt that is KF singing.)

The ending is pretty good: each woman gets what is best for her. Also good: DD acts up a storm, both as the aspiring actress in the film, and as the person in the film. KF is always good. I'm tempted to give this a 7, but the plot is too hokey.

Universal, dir. Seiter; 6+