The maiden names of both of the mothers- in- law were: Kaye Balotta (Kaye Buell) and Eve Windsor (Eve Hubbard).
When Rickles starts to ad-lib ("You're getting on my nerves."), Eve Arden and Kaye Ballard barely hold it together. It's evident that they're laughing.
Rickles isn't really playing the violin, but Kaye Ballard is really playing the flute.
The title is the signature show from the 1946 Irving Berlin musical Annie Get Your Gun (1950), the unofficial anthem of the entertainment industry and an Ethel Merman standard.