Do you give your son a birthday cake when its his birthday? They're full of artificial sweeteners, sugar, colourings etc, but I cant imagine you are going to tell me you give him a plain cake for his birthday?
Fish fingers aren't going to hurt him, and neither is a glass of coke. Its bad of your mother to undermine you, but perhaps she thinks you're being a bit too strict about what he eats and drinks? Did you not eat that kind of food when you where younger?
One thing parents do i've noticed, in my experience at least, is to not buy things for their children to try simply because they dont like the food themselves
my mum doesnt like cheesecake, so we never buy cheesecake, point is, you need to avoid imposing your choices onto your children, because they wont learn how to make choices for themselves properly, they'll always turn to you, or worse, when they get to an age where you cant watch their every move they'll try things that they know you wouldn't allow and rebel against you, which can be disastrous.
Your little boy is clearly following your example and upholding the rule of no fizzy drinks, but is he simply following it because its your choice or because its his choice?