An American film where the man puts on a record and dances with the baby at the end to get her to sleep. The mum then comes in and dances with them. Think it late 80's 90's film. Please save me from wondering!!

Don't remember that exact scene - but maybe Mr. Mom?
Mr. Mom (1983) - IMDb (http://www.imdb.com/title/tt0085970/)

"Nine months" with Hugh Grant and Julianne Moore?