Are the blocks coming apart at the stitch lines? That's what it looks like on the first picture. If that's what it is a good quality hand quilting thread should have you right as rain, you can use a hidden back stitch and fix it.
If it's from use and the fabrics are thinning and tears from the seams, take it to a restoration quilter (call one of your local guilds for recommendations) or LQS for help in finding someone.
You CAN use the iron instuff but for the integrity of the quilt and the age....I would try to restore it as much as possible to orgin. Are there labels on them?