In reading the column and the responses, I noticed a few things that I found interesting that never occurred to me before. 
Red33: "You may wish to reconsider as your gifts may simply not be wanted."
"Your daughter-in-law may well be overwhelmed and/or feel unease at not being able to reciprocate."
dbns: "We're all glad she's stopped giving gifts - now if we can just get most of the rest of the extended family to follow suit."
Those intelligent comments, plus the general sentiment that you should stop giving gifts if you aren't being thanked all provide an answer: Stop giving gifts. But not in a mean-spirited way (i.e. that'll show HER) but because there might be reasons she doesn't say thank you that you haven't thought of.
Don't choose the option provided by the columnist, and here is why: alanauer and several others: "Follow the columnist's suggestion only if you want a lifetime of awkwardness and resentment. "