Trying to convince them will not work. You must take charge and physically throw out the sugar, throw out the donuts, and physically bring healthy foods into the house. Do the shopping instead of relying on your wife to buy the groceries. Tell, don't ask, your wife and relatives what will and what will NOT be allowed to be consumed by your child. You understand that this is serious, they don't. If your child was about to touch a red hot stove you wouldn't ask your wife if you could grab your child, you would physically remove the child from the stove. The most important thing is to DO IT, second is to educate your child and your wife and your relatives why you are doing it. Not the other way around because it will get you nowhere. Take an active role, not a passive role in your child's health. Your wife and relatives have been conditioned their whole lives to eat crap and your child is being conditioned in the same way right now, unless you stop it and set her on a correct path.
A bad diet as you descibe will cost your child in mental and physical health, including the downward spiral into cavities, fillings, mercury, bisphenol-a, behavioral drugs, psychiatric and medical abuses, diabetes, glycemic problems, depression, etc etc etc... It is child abuse and if you do not change it you will be guilty of the same.