Coats & Clark thread is made with short-staple fibers. Long-staple threads, such as King Tut, are stronger because there are fewer places for them to break.
Also, I am wondering how far apart your quilting lines are. Quilted lines 8 inches apart will be under a lot more stress when someone sits on the quilt than quilted lines 2 inches apart.
The "coming undone" problem may be related to how you fastened your ends. If you did not knot and bury ends, or stitch in place for a couple of stitches, or make tiny stitches at beginning or end of your line, this would allow the thread to come loose.
Although you can use heavier weight yarns for quilting (such as 30wt), it's more common to use 40wt or even 50wt.