One way to support the seams from coming undone is to quilt along each one with small stitches, within and through the seam allowance fabrics underneath, either by hand or machine. I do see some 1930's fabrics in the quilt, so your timeline is accurate, I think. Another way to keep seams intact and preserve the life span of any quilt is to only soak when you clean the quilt. Never agitate, either by hand or machine. Also, never dry clean. So sorry about your grandmother's health problems. It may be good therapy for you to finish this top, and it will certainly honor whoever created it.