The T&Q is a super bulky and the Chunky is a bulky. I think the yarn you have should be fine though. 70 stitches on a size 11 is going to be pretty large I think, even though the ribbing stretches. Go ahead and try it - CO as written and work about 3" and see how it looks and what it measures unstretched and stretched. Then decide if the fabric works and if you need less stitches. Unless her son is a teenager, the hat might only need to be 17-18" around, not 20"
sue- knitting heretic