Sometimes (particularly in British English) we can vary whether we use the singular or plural verb in these cases. It can change the meaning though. Remember that the singular verb is used when we are thinking of the group as a whole single entity. The plural verb can be used when we are thinking of the individual members of that group. I would interpret your sentences:
I agree with the advice given -- but another possiblity that avoids the is/are decision entirely is "I have a big family." (or, if you want to make it perfectly clear that you are talking about your parents and siblings instead of your spouse and children, "I come from a big family.")