@HumblePants Yup, two great songs. A little note regarding "Fly Me to the Moon", though: the song was written by Bart Howard and first recorded by Kaye Ballard (while still titled "In Other Words"). But indeed, Sinatra's version is the most famous.
https://www.youtube.com/watch?v=dJ4yJM-vquw is the most popular recording of "On the street where you live" by Vic Damone, and is mostly likely the version that the mom was listening to.