Welcome. I'm sorry that you are in such an awkward situation with you family. In terms of dealing with this conference, I can only echo what MixedNuts said (except for the panicking part). I've always found this quote interesting:

Adulthood isn't an award they'll give you for being a good child. You can waste . . . years, trying to get someone to give that respect to you, as though it were a sort of promotion or raise in pay. If only you do enough, if only you are good enough. No. You have to just . . . take it. Give it to yourself, I suppose. Say, I'm sorry you feel like that, and walk away. But that's hard

We have every reason to think that children's beliefs have no momentum - the evidence is right in front of us, they change their minds so often for such terrible reasons. By contrast, the fact that I disagree with another adult is not particular strong evidence that the other person is wrong.

In other words, try to free yourself from feeling obligated to defend anything or feeling guilty for not engaging with those who wish to change your beliefs. You might consider explicitly saying "Social pressure is not evidence that you are right (or wrong)." If the people talking with you assert that they aren't using social pressure, then ask them to stop continuing the debate. Their willingness to leave is a victory for your emotional state, and their refusal is strong evidence that arriving at true beliefs is not really their goal - but the proper reaction to that stance is to leaving the conversation yourself, not try to win the "you are being rude" debate.

In short, maximizing your positive emotional state doesn't rely on winning debates. Your goal should be to avoid having them at all. (If you hadn't already read the book your father found, I would have suggested declining to do so).