Unless your family has a legit reason to disapprove (like your cuz is on drugs or something) this is none of their business. Also, why do you put "son" in quotes like that. He IS her son.
Also, you don't give your age, but if you're a minor teen, just promise yourself you won't grow up so petty and ignorant. If you're an adult, you're free to include whoever you want in your life. If she doesn't qualify because she adopted a child, leave her alone. She's better off without you and so is her child.