Answer

A fascinating question. I thought about it a bit, and this is what I’ve come up with so far.
 
If it is permitted to harm the mother against her will, that could only be because she has the status of a pursuer. Otherwise, we do not harm one person (even harm that does not involve death, such as taking an organ from someone by force) in order to save another.
The law of a pursuer with respect to the mother requires clarifying two points: (a) Is the fetus a person, such that someone pursuing it would have the status of a pursuer? (b) Is such a situation in fact called pursuit?
On the first question, there is the well-known Mishnah in Ohalot and the Talmud in Sanhedrin, which says that one kills a fetus that endangers its mother, but once its head has emerged one does not kill it. That implies that the fetus is not a person. But in the plain sense of the Talmud, the permission is not because of that, but because this is not a case of pursuit (“He is being pursued from Heaven” — meaning, Heaven placed him in this danger). If so, these are exactly two interpretations that disagree on the two questions I posed above. One bases the permission on the fetus not being a person, and the other bases it on the fact that such a situation is not pursuit.
But Maimonides uses somewhat ambiguous language there (he bases the permission on the fetus being “like a pursuer,” not on its not being a person). This runs against the plain sense of the Talmud, which says it does not have the law of a pursuer (the proof being that once it has brought out its head, there is no permission to kill it). In my view, the simple reading of Maimonides is that there is a law of “like a pursuer” here, which permits killing the fetus to save the mother only because its life has lesser value. That is, according to his view the permission is based on both components, and both are required: the life of the fetus is worth less, and the situation is a kind of pursuit. If one of those is missing, there is no permission.
But now we have to discuss the opposite situation: does the mother have the status of a pursuer with respect to the fetus (or perhaps “like a pursuer”), just as we saw regarding the fetus in relation to her? At first glance, Heaven put him there and also put her around him, so this is not a case of pursuit (but perhaps of “like pursuit”). But one could distinguish between them, because the fetus is there against its will (from Heaven), whereas the mother decided to bring it into the world, and she is the one who put it there. From that it follows that with regard to the mother’s pursuit of the fetus, it may not be applicable to say that “Heaven pursued him,” and therefore the mother may indeed have the status of a pursuer toward it. True, the danger was not caused by her but by Heaven, but his very presence there is because of her.
My own reasoning would be that the mother does have the status of a pursuer in such a situation, because she decided to bring it into the world, and therefore responsibility for its welfare and life is in her hands, and if she can save it, that is her obligation. However, the value of the fetus’s life is not that of a complete person, and therefore even if we decide that the mother is indeed in a situation of pursuit, we still have to ask whether the law of a pursuer applies to her, since she is pursuing something that is not fully a person. Perhaps in such a case there is no permission to harm the pursuer. Still, since this seems to me to be a full-fledged case of a pursuer and not merely “like a pursuer” (because she put it there), perhaps even where there is danger to the life of a fetus one should permit, and even require, harming the pursuer (the mother).
Regarding the value of fetal life, see the survey here:
https://din.org.il/2020/01/17/%D7%A9%D7%9E%D7%95%D7%AA-%D7%93%D7%99%D7%9F-%D7%A8%D7%95%D7%93%D7%A3-%D7%91%D7%A2%D7%95%D7%91%D7%A8/
There too he discusses Sabbath desecration in order to save the life of a fetus. Practically speaking, halakhic authorities rule (in the Shulchan Arukh) that one desecrates the Sabbath to save it. And seemingly, by the same reasoning, the same would apply to a pursuer after a fetus — that it is permitted, and required, to kill him.
However, this too requires discussion, because the obligation to desecrate the Sabbath could be based on the reasoning, “Desecrate one Sabbath for him so that he may keep many Sabbaths.” (True, that reasoning is rejected in the conclusion of the Talmudic passage in Yoma, but only because it is insufficient in cases of doubt. In fact, in the passage in tractate Shabbat 128, if I remember correctly, it is indeed brought regarding Sabbath desecration to save a minor. And seemingly the same applies to a fetus, which is destined to keep many Sabbaths.) If so, then it is not clear that one can infer from the obligation to desecrate the Sabbath in order to save it that there is also a law of a pursuer regarding someone who comes to kill it.
As a side point, there is room to discuss a different risk to the fetus, one that is not death. It may be that if you combine the fact that the danger here is not death, that we are dealing with a fetus whose life has lesser value, and also the doubt whether such a situation is even considered “like pursuit” at all (or whether “He is being pursued from Heaven”), then it is not entirely clear that one can obligate the mother to undergo surgery. But at the same time, one must remember that with respect to the mother as well, this is not a matter of killing her, but of requiring her to undergo surgery, which admittedly carries risks, but is not truly a very dangerous surgery.
Bottom line, I would say that according to Jewish law the mother is obligated to undergo the surgery, and that is how one should rule for her. Even so, if she still does not want to, it is hard to force her to undergo surgery against her will. In my opinion there is strong reasoning even to permit coercion (like coercing a parent to feed the child after it is born), but the burden of proof is on the one who would extract that from her. Perhaps one should distinguish between a case where the mother claims that the refusal is due to the risk to herself — in which case one cannot obligate her to endanger herself — and refusal due to inconvenience, where it is easier to obligate her (after all, feeding a child is also inconvenient for parents).
That’s it. Just some initial lines of thought. It is rather surprising that so far I have not found a discussion of this, though of course that is no proof. I sat on this for only a few minutes just now.