I know how hard it is when you can see so clearly what needs to be done, but his mama won't listen.
Tantrums are typical for this age group, but you are so right! How you handle them determines what the child learns. If he is always given his own way...it is giving him the wrong message - throw tantrum = get own way, and he will take this into adolescence and adulthood. Of course you already know that but you voiced your concern, and I guess for now, just have to make attempts to correct him the proper way when he is in your home or you are baby sitting.
It is definitely a fine line to walk between gram and mom....best of luck.