The new manager says, 'attending this conference is "a condition of your employment here"'. The old manager already decided it wasn't essential that you be available that week, and you have that in writing in the form of the original approval for the leave. You have a bus factor of 1 on your job and you're willing to quit. The new manager hasn't (as far as you've said) even explained to you why she thinks this conference is so important, so she appears to be demanding blind obedience at great personal cost to yourself.
So, unless your new manager knows something you don't, to explain why she's trying to get you to quit, she's made a tactical mistake here. Maybe she, rightly or wrongly, knows one or two people that she would like to hire to do your job. You don't know for a fact that she needs you, so you'd better be serious about leaving before mentioning it to anyone in your company. Anyway, most likely is that she's misjudged the situation and thinks you'll cancel the trip if she leans on you.
I disagree with the answers that say your first response to this mistake should be to go to HR or your old manager. OK, so your new manager has started out by setting an extremely hostile and uncompromising tone for your relationship. Maybe that's what she wants, in which case one of the two of you will be leaving sooner rather than later. But if it's not what she wants, then letting her "deal with it" (that is, change her mind gracefully) will tend to defuse the situation. Proving in front of witnesses that her authority over you is not what she thinks it is, will tend not to.
Your first move should be to convince your new manager that your old manager and you both know what you're doing, and that you aren't needed at the conference. So, go to her and say, "this has been considered before, the leave was approved by the company, I have committed to the trip on that basis, and the trip can't be moved because it involves four people with leave booked from four different employers. I don't think it's essential that I attend the conference, [if you already discussed that conference with your old boss at the time you booked the leave, insert here the agreed reasons]. In any case, I can't attend the conference because I'm committed to my trip."
It's now her choice. She can back down, in which case the negotiation is over, or she can stand her ground and repeat that the company requires you to attend the conference as a condition of your employment. If the latter, then someone else needs to be pulled in to sort it out.
If your old boss was promoted directly upwards, and therefore is her boss, then he's in a better position to change her mind than you are. So, the next step is to go to him, on the basis of your existing relationship and the fact that he had already authorised the leave, and let him understand that there's a serious problem going on under his authority. This is "going over your boss's head", with all the drama that implies, but her contradiction of his decision is precisely the kind of situation where going over her head to her boss is appropriate.
If he's been promoted upwards and elsewhere, then he might not be any use, other than to officially confirm that what you're saying about your past discussions with him is correct. Or maybe to give you personal advice how to deal with the situation given that he knows a lot more about it that I do! If he can't help you, you'll have to go either to her boss or to HR, whichever fits better with your company's usual way of doing things.
If you do formally complain, then your complaint is that she has threatened to fire you over pre-booked leave that you're committed to taking. HR is going to look both at whether the company legally can do that, and even if so whether she has the authority to do that on behalf of the company, and even if so do they agree she's done the right thing by making that threat. So, the more of those questions you know the answer to in advance of making the complaint, the better. If you can get that threat ("attending is a condition of your employment") in writing then that's much simpler for your complaint than if it's just verbal. As against that, if it's just verbal then you might literally be able to ignore it. She can't fire you without ever writing anything down.
Also, be prepared that if the company does back her, you need to pay attention to the terms you're leaving on. Even if their demands are ridiculous, it's generally better to quit than be fired, except perhaps in the extreme where you plan to make a legal case of it. Depending on company rules, you might not be able to use your old boss (and other colleagues) as a worthwhile reference, especially if the company decides to fire you before you quit, so take into account what happens next. If you are concerned about retaliation from HR or whatever, then it might even be best for you just to quit without ever escalating to them: there's no point involving anyone you think will take her side.
The fact that the job is otherwise good suggests that this isn't a big risk, and probably the company will back you, but even good companies can occasionally surprise you with how seriously they take the heirarchy. Until they agree that she's well out of line, the default assumption of most higher-level managers is going to be that they don't want to keep a dog and bark themselves. So, if there's a lower manager in position then that's because middle/senior management doesn't want to have to make decisions about leave. In this case you have going for you that your immediate manager at the time already made this decision, and she's trying to reverse it. So, respect that this isn't about whether or not she has authority to approve or refuse your leave (because of course she does). It's about whether not the company backs her in revoking assurances the company already gave you, and which you have heavily relied on, and which the company (in the form of your old boss) knew you would heavily rely on when it gave them.
Ultimately, you already know what your own position is, so this whole negotiation is about whether your new boss, and the company as a whole; (a) want to force you to say you're prepared to quit over this; (b) want to call that threat (or, as they hope, "bluff") once you've made it. I think your first moves should avoid even (a), because once you've threatened to quit a job there's no guarantee you can get back to a place where your employer feels they can rely on you. So, try to get the need to quit off the table and then you won't have to tell them that you are prepared to quit. That said, if your new manager really is as bad as all that, then one or both of you is leaving soon anyway, in which case it doesn't really matter what she thinks of you!
