All 3 are correct. "Herself" sounds best since you have already mentioned "her". In English, there are pronouns that act as objects, and pronouns that act as subjects: "I saw him". ("I" = subject and "him" = object") "He saw me" ("He = subject and "me" = object) However, with the verb "to be" you have a choice. You can say "It is I" or "It is me". Both are correct, though in certain contexts one might seem better than the other. For example, in this conversation "Who hit the ball?" "It was I" "I" works better because "I hit the ball", but "me" is really wrong. You can even use both pronouns: "Me! I'm the one who did it." Or, consider this phone call: "Hello, could I speak to Heidi?" "This is she." I was always taught to say it that way, but some people will say "This is her". Some people will insist on doing it one way or the other, but I don't see any logical way to determine who would be right.

I would suggest: They're her dad, her mom and her. People do sometimes use the reflexive pronoun "herself" in this circumstance, but you certainly wouldn't want to do so in formal writing. The object pronoun "her" is the grammatically correct choice.

A surprisingly interesting question. There are a number of options. Natural to me are: They’re her dad and mom, and herself. They’re her dad, her mom, and herself. Her family consists of her and her parents. Her family of 3 consists of her and her (two) parents.

The first sentence much better