Howdy Anitar,
You can find a summary here: http://www.jehovahs-witnesses.info/sscc27.html
As you recall the fundamental issue is one of "Christian Neutrality." JWs believe or rather believed that a true Christian should not involve themselves with or compromise their neutrality when it comes to matters of politics and also the military. Malawi dealt with political cards and Mexico dealt with papers (the Cartilla) that verified military training. In Malawi, the Witnesses were (instructed) not to buy the cards and in Mexico the Witnesses were (instructed) that they could obtain the cards, usually through bribery.
(This was of course pre-revision of the alternative military service and compulsory civil service viewpoints (doctrine) and pre-revision of the "compulsory voting" viewpoint (doctrine) which probably would change things today.)
"Proving" this to your mom is going to be somewhat difficult. The treatment and situation of the Malawi Witnesses is easy to show from publication excerpts and from Yearbook accounts, so that side of the "scales" is easy enough to prove to your mother.
The difficulty comes in showing how the Witnesses in Mexico were treated in a completely different way and how they were permitted to obtain their cards, perhaps through participation in the (reserves) military training and more often through routine payment (bribery) of government officials.
To my knowledge, no OFFICIAL WT publications have ever even discussed the compulsory reserves military training, much less discussed how JWs either view it or what they do about it. Thus if the ONLY INFO your mom is willing to consider is Official WT literature you may be out of luck.
It is possible to prove the issue to her, if you or her KNOW any Mexican Witnesses who faced the issue and who know of the situation and who will candidly tell your mother about it. That first-hand testimony may be the only way to convince your mother.
You could also possibly TRY writing the Society and asking them NAIVELY about what their directives were to the Mexican brothers at the time and see if you get any contemporary letters that will admit what the policies were, but that is extremely unlikely to produce the evidence.
Otherwise, your mom will have to rely upon the veracity of the copies of the documents that are extent, including what was republished by Ray in CofC, that show what the official position and directives were to the Mexican Witnesses. All these copies though are going to only be available on websites or from sources she would view as questionable.
-Eduardo
PS: while you are on the subject, you might find it good to bring up what I call the "Mexican Question" which basically discusses the perplexing reason why the Witnesses were organized as a cultural association instead of as an official religion for most of the 20th Century. There are a lot of "official" citations that you can provide to show her about that topic.