I hope you don't mind a quick opinion from a WS. IMO, it is the WS's burden to make the effort(s) needed to "make things right" and restore trust after infidelity. In much the same way that, if a person hit a baseball and broke your window, it would be their responsibility to get that window fixed. Would you hire a PI to follow the window-breaker and make sure they aren't out breaking other windows, or spending their window money on something else? No, of course not. If they don't get it fixed, so be it, but the window-breaker will no longer be welcome in your life, and never trusted again. It isn't a punishment, it's a consequence.
Clearly, you are not at all comfortable with her going on this trip, which says to me that she has not done enough yet to prove to you that she is a safer person to be around. I imagine it doesn't feel very good at all to have to play the role of policeman and parent with your spouse. It shouldn't be your burden and your expense to check up on her, she should be the one working to prove to you that she's changed, and isn't the kind of person who would cheat anymore. Going off on a drunken girl's weekend near the OM and near his birthday... tells me she's not even close to being safe. She is not thinking of you, your needs, your pain, your fear... she is only thinking of herself. Which is exactly what she was doing when she had the affair in the first place.
What is hiring a PI going to do for you? To determine if she's a cheater? I can save you the $$$. She already cheated, she already lied, she already betrayed you. She is a cheater. No PI needed. Are you trying to determine if she's STILL cheating? In my opinion, whether or not she's currently/physically having an affair is not really the question that needs answering. If a cheater wants to cheat, they will, period. So the real question (in my mind) is, "Is she a safer person now than she was before? Has she put in the effort to change and be someone more trustworthy, more caring and empathetic, someone who respects themselves and yourself too much to cheat again?". If the answer is no, then she is still unsafe, still a cheater. If she isn't cheating now then she will be later. Or she will continue to lie to you, put herself first, make the wrong choices. Honestly, if you really mistrust her that much, then I'm just not sure what a PI is going to do to make that any better for you? Let's say you hire him and he follows her on her weekend, and she doesn't cheat. What then? Is it over? Do you trust her now? Will you not break a sweat the next time she goes away? Do you keep hiring PI's for the rest of your marriage? Where does it end?
My take would be this... she should not even be asking about this, let alone going to it. If her weekend away is more important than fixing the relationship with you, then you have your answer. Don't hire a PI, hire a lawyer. Wish her well on her trip and ask her where she'll be staying afterward since she won't be staying with you.
Look, she might honestly have zero intentions of visiting the OM or anything else. It doesn't matter, that's not the point. The point is, she's not thinking of you, she is not putting your safety and your needs first, and she's not putting in the effort and sacrifice needed to make the changes to become a safer person. Hiring a PI won't fix any of that. Won't prevent it either. Worst that happens is that she goes to see the OM, the PI catches her, tells you, and then... what? You already don't trust her, do you really need to re-validate that perspective? DO you really need the new mind-movies to torture you?
She didn't need help to figure out how to cheat on you. She put in the effort needed to get her way, and the effort needed to cover it up. And she succeeded in those goals, right? So we know she knows how to work hard to get what she wants. If she wants to R with you, then you should see her putting in that same level (or more!) of effort. And if she is, you'll know it. She doesn't have to succeed for you to know she's trying, so clearly she is not.
This is just my advice, take it or leave it. My only suggestion is that you take a step back, and ask yourself what problem you are really trying to solve here, and what is really best for your own emotional health and well-being. You've already been traumatized by having been cheated on. Don't continue to allow that, and don't make your own life harder and more painful. Every BS has to decide for themselves if they want to D or R. The thing is, every WS has to make the same decision. And both BS and WS must be wholeheartedly "in it together" to successfully R. If that's not the case, and if efforts aren't being made by both people to R, then there's no point in wondering how R is going. It's not. There is no progress when there is no effort.
Try saying this to her, "Look, I'm not at all happy about this trip, but more than that, I'm hurt and angry that you even thought to go in the first place. This is hurting me and upsetting me, and you can see that, but you still aren't able to put your own desires aside, not even for my well-being, not even after you decimated me. I want you to think about this long and hard, and decide now, once and for all, if you want to try and make this marriage work, or bail. Because I'm done worrying about where you are and what you are doing when you can't show the same level of concern and effort back. If you want to go, then go, I won't stop you, but I'll also do what's best for me without regard to you want, which likely means calling my lawyer. If that's not what you want, then make a different choice, and convince me you really want this. Because right now it feels like it felt before, and that's not acceptable."