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Love and attention are all that is needed as we all know, however, if your Mother spoils your Children (Son) why not allow them both these actions in moderation; without saying a word, given it is a short time that your Son will have his Grandmother around to do these things and your Son will have these beautiful memories in his life for later when hardships really begin.
Perhaps take your Son out of the home more often to the park and other entertainment venues, mixing with Children his own age, reducing the time spent around his Grandmother treating him too much.
That way, your Son will be unable to continue with tantrums within the home and where his Grandmother can hear the tantrums, reducing any negatives in all of your relationships.
When your Son commences a tantrum, teach him that it is unacceptable by going out for a walk (he will learn that there is no audience and he cannot get your Grandmother’s attention and will give up on these), a drive somewhere/visiting friends, playing in the backyard, another distraction, or to his room.
Why not offer a reward system based on the Clock approach and in complete unity with Grandma (your Mother). After your Son has played or done chores (I am not sure of your Son’s age), at morning tea, if his behaviour is fine, he receives a treat from Mum or Grandma. If he has put on tantrums for treats; out he goes playing again until lunch time; the treat will not arrive until afternoon tea time. If he continues with the tantrums; no treat at all that day from either of you. The next day, your Son does not receive a treat given that you and Grandma have agreed that treats only arrive on Mondays, Wednesdays and Fridays for example. A calendar could be put up on the wall or in the kitchen for your Son to understand if he is 4yrs of age+ to comprehend it all.
The first couple of days filled with tantrums are the most difficult as you know, however he will soon learn that putting on tantrums has the opposite effect in which he will not be receiving any treats with that type of behaviour not tolerated by either yourself or his Grandmother (suppressing the treats). If your Mother loves and respects you, wants the best for her Grandson, she will agree.
You are his Parent and Grandma is wonderful for all of her beautiful Love and Support to her Family, however treats are just that; a gift on the odd occasion throughout the week; not on a daily basis.
Your Mother is a wonderful Mum having you and her Family live with her.
Love and best wishes.