When Lucy arrives home in New York and is greeted by her neighbors she passes Little Ricky off to a woman. That woman was the real mother of the twin boys who portrayed Little Ricky.
The title or plot of Ricky's movie is never mentioned. Ricky says that the premier will be held at Radio City Music Hall in February; however, except for one reference in a later episode when Lucy says, "I wish you never made a movie," the movie is never mentioned again, and Ricky never makes another movie. This plot point, in the context of the show, was supposed to be a springboard to a film career for Ricky. From a production standpoint, it was simply an excuse for the writers to place the characters in Hollywood so that they could have a plausible reason for having Lucy tangle with so many movie stars playing themselves. Once the Ricardos and Mertzs returned to New York, the movie-career plot point was no longer needed and dropped.