If I ask the journal to remove my name from the author list, will they simply do it?
No one can say other than the journal, but personally I find your wish unreasonable. The fact that you are a coauthor of the paper is now a historical fact and as such not subject to change in my opinion. Keep in mind that even when a journal retracts a paper, they don’t pretend they never published it, but rather issue a statement saying they no longer endorse the validity of the paper. This preserves a record of the historical events that occurred and maintains a sense of continuity of the picture of reality the journal presents to its readers and to the world.
Similarly, if one of a paper’s coauthors no longer stands behind the validity of the paper, I would expect the journal would at most append to the article a statement saying that you no longer wish to be considered a coauthor of the paper. But it would be dishonest of the journal, and would be doing a disservice to its readers and to historical accuracy, to pretend you were never a coauthor by simply airbrushing your name off the author list.
So, my feeling is that you are free at any time to disavow your implicit endorsement of the paper that comes with being a coauthor. You may not even need the journal’s help to do that - for example, you can post a statement that you no longer endorse the validity of the paper on your personal web page. And you can also ask the journal to post the same notice online next to the published paper - hopefully they will find that a reasonable request, and perhaps it could motivate them to investigate whether the paper contains fraudulent data. But I think it’s dishonest to pretend you were never a coauthor of the paper, and unreasonable to ask the journal to carry on such a pretense.
Finally, keep in mind that “Pat”’s dishonesty is her own. If you unwittingly coauthored a paper in which she committed fraud, that would make you a victim, not a perpetrator, of misconduct. I don’t think it reflects poorly on you that you fell victim to such fraud (if indeed that is what happened), as long as your own work on the paper was done in good faith, and you had no knowledge of any fraud or other unethical behavior on the part of the other authors.
Edit to address the comments about the last part of my answer: I understand some people feel OP is partially responsible for the contents of the paper as a whole including the contributions of their coauthors. That’s true up to the point where OP read the paper, spent a reasonable amount of time informing themselves about what the other coauthors did and how they did it, and were not aware of any suspicious signs that anyone was doing anything improper. That’s basically a very low bar of responsibility to clear in my opinion, and certainly far from what is actually needed to prevent all occurrences of fraud in a paper you are coauthoring. Beyond that, if it turns out that there was misconduct, of course it’s embarrassing to OP and they are right to be concerned and to think about how to protect their reputation, but I don’t think any reasonable person is likely to hold what happened against them, so I don’t think they need to be very concerned.