Re: My mother's 1956 Buffet Crampon Alto Sax
1956 would probably make it a Dynaction model. These are great saxophones and considered professional models. Don't sell it if there's any chance that your daughter may play saxophone in the future. You'll waste a lot of money renting and/or purchasing and you'll end up with a horn not half as good as the Buffet you currently have. What an advantage she would have starting on a great instrunment as opposed to the "throw away" saxophones that many music stores sell as "student" models today.
1950's French craftsmanship was extrordinary. Both Buffet and Selmer were coming into the top of their game with both saxophone and clarinet manufacturing!
The actual selling value of your sax today doesn't reflect how good it really is. You may get $1000-ish for it in "as is" condition to the right buyer (assuming that its in decent physical condition and original lacquer) and maybe $1500-$1700 fully overhauled. However, comparable new professional model saxophones today sell for $2500 and up.
Don't let someone talk you into selling it cheap. These are great horns that play well in tune with modern keywork and have an excellent voice and response. Check out the attached 50's ad of Jackie McLean playing a Buffet Dynaction. Jackie was one of the giants of the jazz bebop era.