After his estranged ex-wife dies, Tom Winters (Cary Grant) is left with three children he barely knows. They are not getting along well.  Younger son Robert runs away, and meets Cinzia (Sophia Loren). Cinzia is a 24 year old Italian lady, touring America with her father.  Like Robert, she is also running away from a distant domineering father.  When Cinzia brings Robert home, Tom mistakenly thinks she is poor and homeless.  The kids love Cinzia, so Tom hires her her as a housekeeper.  In a complicated plot development, they all end up forced to live on a dilapidated houseboat.  They gradually repair the houseboat, until it is beautiful by the end.

Cinzia is in love with Tom, but Tom is clueless.  The dead ex-wife had a younger sister, Carolyn.  Carolyn shows up boldly stating she has loved Tom since she was a young girl and he married her older sister.  Carolyn wants to marry Tom now that her sister is dead.  There is a high society dance at the country club.

When Cinzia, as a housekeeper, is treated rudely , Tom finally realizes he loves her.  Carolyn accepts that Tom loves Cinzia, and that Tom was never meant to be with her.  The children are initially opposed to the wedding, because they think they will lose Cinzia as a friend.  Eventually, they warm up to the idea.

The movie ends with the wedding of Tom and Cinzia on the houseboat.

Thanks Joseph C!