I am aware of the "controversy" - I do not consider them equal variants however - as an attorney (at least here in California), I have never seen the "judgement" spelling used in legal work. I think it would be safer for Zac's Mom to use "judgment" for an American audience : )
I agree about the safety of using "judgment" for an American audience. Safety is an important consideration.
It is also good to remember that the WWW and other media have had an international audience for a good number of years and, even apart from that international influence, our language is in flux.
It will be interesting to watch the ways in which American English will become more like British English and vv.