Christmas gift for by proxy?

This is my second Christmas post-breakup. Last Christmas, I took our boys, then 13 and 15, to purchase gifts for their mother, my ex-wife, who cheated on me with a co-worker and left me for him. (Don’t feel bad for me, he’s a fat guy who wears shorts in the winter, so whatever.) Anyway, I had every intention of taking the kids out gift-shopping for their mother again this year, but she has asked “them” to buy her some necklace that’s $130+. Last year’s budget was $40 each, which I thought was generous considering the situation. My questions are: Does this not seem like a gift “from me” by proxy of the kids? How do address this with the kids so as not to sound petty? I’m already losing 1/3 of my paycheck in child-support. Tell them I just can’t afford it? Thanks for reading.

EDIT: Sorry I borked the title.