One option is to NOT tear it apart. Treat the quilt with no batting as a quilt top. Sandwich it with a new batting and a new backing and requilt it. If you plan on hand quilting it you can do a section at a time. It is up to you on if you want to leave in the original hand quilting and simply quilt next to it or over it. If I were to tackle such a job, I would leave the old quilting stiches alone and simply hand quilt over them or right next to them. If I were to machine quilt it I would probably do the same thing. This way you don't have to worry about damaging the original by removing stitches. Be advised, by doing this you will destroy or seriously depreciate any monetary value the quilt has as an antique but it sounds from your post that it is sentimental value to you and in that case, if you want to continue to use it then don't worry about what refurbishing might do its value as an antique.
Edited to add, by doing it this way you will have to bind it, unless you "birth it" but I would worry about wrinkles if done by "birthing".
Last edited by feline fanatic; 07-18-2012 at 06:17 AM.