Ally, although you feel like a family, and in my opinion you are, I don't think a Family Visit Visa covers your relationship.
As you say, you haven't been living together. So I think a General Visit Visa is the right way to go at the moment.
You should, of course, explain your situation regarding your relationship, and your son. To all intents and purposes (other than the name of the visa) the application will be exactly the same.