Conservative neck liposuction
As long as you are adhere her ideal body weight, and has a diet resistant fat located in the neck, a conservative liposuction procedure can accomplish reducing the double chin.
Unfortunately, you are correct in that the area under your chin is made up of fatty tissue that you inherited from your parent(s). However, there is currently a very good nonsurgical option which is available that can permanently remove the fat. It is called Kybella and it is a series of injections done about 8 to 12 weeks apart that dissolves the fat. Alternatively, you can do a limited liposuction of that area to remove the fatty tissue. Good luck in your area.