Hi C.,
I have a 17 month old son and he acts just like your son does....totally normal! You definitely cannot expect a child this young to "behave." We do still venture out into kid friendly, loud, restaurants and sometimes he is an angel but sometimes he is a holy terror. What helps me sometimes is to bring some snacks along like raisins or crackers (even if he has already eaten a meal he will still snack on something) to keep him busy. Like I said, sometimes this helps..heheheh.
You can't really do much at this point other than not go out. They are old enough to know what they want to do but not old enough to know what's acceptable restaurant behavior. We couldn't really take my oldest out to a restaurant without fear of being thrown out until she was nearly 3 but my middle son has always been an angel. It all depends on the child.
As far as your mother goes, I would just parent your child as you see fit and ignore your mother's "advice."
Good luck!