Your grandmother's quilt was probably hand quilted. While it would be a shame to pick out her stitching, I would remove it, the backing, and the batting. Then, I would use a light weight fusible web and fuse a pre-shrunk piece of muslin (or an old white sheet which, if you don't have one that you would like to use, are available very cheaply at thrift shops) to the top. Iron on the muslin or sheet side with the quilt down.
I would soak it very gently in a bathtub. First use distilled water to wet the rust stains. Oxalic acid will remove rust; however, if you have hard water it may join with the minerals to form precipitates, which is why I suggest distilled water. You can find oxalic acid in commercial products such a Zud Cleaser (pat, don't rub and abrasive product like this!), Bar Keeper's Friend, and some commercial deck cleaners.
Then I would gently wash it in the tub, perhaps adding a bit of stain remover that you know and like. Rinse and, without twisting, gently squeeze out as much water as you can without stressing the fabric. Spread out your biggest towels on the floor and roll the wet quilt top in them, press out more water, and air dry.
This may give you more salvagable pieces. You could requilt them and frame them. A larger piece might make a backdrop behind a bed. Smaller pieces could be framed in a grouping.