First off, you haven’t committed a crime (assuming she was above the age of consent) and you haven’t engaged in academic misconduct (since there is only an indirect academic relationship between you). However, the fact that she is threatening/blackmailing you is very concerning. The fact that she is your advisor’s daughter makes things more complicated, but being threatened or blackmailed by a sexual partner would be deeply concerning in any circumstance.

I do not know the exact nature of the threats or blackmail, but I would not engage in a relationship with someone who is threatening or blackmailing me. Only you know the exact situation, but your choice of words rings alarm bells. My primary concern in your situation would be worrying about whether she will make worse threats — e.g., false rape accusations. That would be much worse than a spat with your advisor.

If I were in your situation, I would try to record my conversations with her so that I have some evidence to protect myself if she does carry out her threats. Save text messages and get a voice recorder app on your phone. (Check the laws on recording conversations in your state first.) The only thing other than “he said, she said” you have to defend yourself is such evidence.

Maybe I'm misreading the situation from your question, but your choice of words "threatening" and "blackmail" is concerning. And there is no harm in trying to protect yourself from possible future accusations. Hope for the best, plan for the worst.

This is not a complete answer, but I think you should worry about being threatened/blackmailed before you worry about dealing with your advisor.

In terms of dealing with your advisor, two (conflicting) points: Generally, honesty is the best policy (as Buffy's answer emphasizes), but she is an adult and her father has no automatic "right" to know about her sex life, and there is a good chance both of you would prefer him not to know (as Nicole's answer suggests).

In terms of dealing with her: It sounds like you are still on speaking terms with her and you should absolutely try to talk things through with her. Treat her with respect and acknowledge her feelings. (See Geoffrey’s answer.)

It may be worth thinking about the contrast between this:

I could not resist her. I am here alone and had not been with a woman in two years until then.

and this:

Now she wants to start a relationship with me and is threatening me to tell his father, which is my PhD advisor, that I seduced her

Perhaps she sincerely believes you did seduce her. If you felt unable to say no to this encounter, which you now regret, is it possible that she also felt unable to resist?

Here is one possible scenario (I don't claim it's the only one) that might explain her reactions:

You're six years older than her. She's known you since she was a child, and you're part of her father's social circle. (The power gap between you and her father probably isn't as visible to her as it is to you; when I was a kid and my father had his PhD students over for dinner, I tended to think of them as "Papa's friends", not as his juniors.)

She probably doesn't see that you're lonely and haven't been with a woman in two years, nor that you view yourself as somebody who's awkward with women. She probably also isn't factoring in how alcohol might have affected your judgement, especially since she's not even old enough to buy alcohol herself.

What she sees is a guy six years older than herself, almost a PhD. From a 19-year-old's perspective, mid-twenties seems very old and mature. She probably had more faith in your maturity and judgement than you do yourself.

Then she slept with you, and things didn't end up the way she had hoped, and that hurts. So how does she interpret that hurt?

From her perspective: you are a very old and mature person, so presumably you knew how this was going to turn out. Therefore, the fact that she got hurt is perceived as being due to callousness on your part - you took advantage of her, "seduced" her. She may find it hard to comprehend that you felt "unable to resist".

IMHO, the best course of action here is to acknowledge that things didn't go the way they should have, take ownership of the fact that you did choose to sleep with her, and express sympathy for the hurt she is feeling. Were I in your situation, I might say something along the following lines:

I want to apologise to you for what happened. I like you and I find you attractive, but I didn't think enough about what us sleeping together might mean to you and I'm sorry I didn't talk to you about that first. You're an adult and I think of you as an equal; I didn't think that you might be counting on me to look out for both of us.

(I'm struggling a bit with that wording, suggestions for improvement welcome.)

Attempting to blackmail you is unacceptable behaviour. But if you acknowledge the hurt and if you can shift her perception of why it happened, you might find that the blackmail issue resolves itself.

If you can't resolve things with her, then you may need to talk to your professor and explain the situation, which is going to be an uncomfortable discussion. But I'd recommend doing all you can to make things right with her first.

One of the problems with conversations about sex-gone-wrong is that the emphasis almost always ends up on "whose fault is it?" rather than "somebody is hurt, what can we do to heal that?" Often the latter is actually more tractable, especially in situations that break down to poor communication and mismatched expectations.

Personally, I would tell her to go for it. There's a pretty good chance she's bluffing. Kids do not tell their parents when they're having sex. If, in addition, she's as you described, "cute and hot", it's far more likely she's merely manipulative than desperate to have you at any cost.

Even if she's not bluffing and does tell her dad, so what. You can't change the past, it is indeed a fact that you had sex with her and I don't see how your situation improves by preemptively "kissing and telling". If you tried going first to your adviser, what would you even say? "Hi, Prof! Guess what? I had sex with your daughter and now she's blackmailing me!" How's that going to go over?

Look at this as a game-theoretic problem: There's no payoff to blackmail unless the blackmailer gets what they want without carrying out the threat. It's a one-shot deal. Once the threat is carried out, it's no longer a threat because the information has been released. If she knows she's not getting the relationship either way and that the only thing that will happen if she carries out the threat is that Dad will know she's having sex, that's not much of a payoff. Telling her to "go for it" explicitly informs her that you intend to ignore the threat and that you will not be swayed by it.

What I would not do is escalate or mirror the bad behavior. If you think responsible adults do not secretly record, collect evidence against and blackmail people they have sex with, then don't respond to that by doing it yourself. Instead, simply end the relationship and end all contact.

Ultimately, you can't control what she says but you can control what you say. If she tells her dad and he confronts you, I would point out that you consider one's sex life to be a very private matter, not something adults discuss with others. I would express surprise and disappointment at his daughter's behavior but otherwise refuse to discuss the matter except to deny any false accusations.