Don't let people discourage you when you are asked to make a memory quilt for someone you loved. How dare they advise you to say a firm "NO". I'm sorry, but that's not right. Your question, was how can I work with the materials I was given, not should I commit this labor of love...
You can also see if the family can provide some cotton to you, so you have a nice foundation to apply some of this non-ideal fabric to. I wish you luck and know you will enjoy the process even if it's not an ideal situation for quilting. Also, if you can only make one or two - they'll appreciate it very much. God bless!