What do you do in situations like these? Regarding my 4 year old nephew?

yes there should be rules yall should set down as a family and dicuss this he is old enough to learn some table manner and manners periord shes not a good mom if she not doing better than that cause as he gets older hes gonna run her not her run him she needs to displine maybe time out and when she does tell him he got 5 mins from the time he stops trowing his temper tantrum. dont let him get up and run around or nothing make him sit there if he gets up add mins to it he will eventally learn, but everyone has to be persistant with doing this. i hope it works out and my advice helps good luck!!!