I am trying to find out the name of an old movie about a mom with two sons. I believe the father was killed while in the navy. The father had given the boys one of the navy signal lights (usually used between ships while maintaining radio silence)and they were using it and attracted the attention of the navy. The mom starts dating one of the officers sent to investigate. Later one of the boys goes up in a weather balloon and they try to rescue him.

A Ticklish Affair (http://www.imdb.com/title/tt0057583/)