No, there are no exceptions, abortion is always and in every case the wrong choice. It is directly and intentionally taking a life.
That being said, if a mother's life is in danger, one can remove the child from her womb if need be (through induced labor or C-section), although this may, depending on the child's gestational age, end in death for the child. But at least in this instant, the intent is not to kill the child, it is to save both mother and child if possible.
This is different than giving drugs to directly kill the child, or killing the child in utero with instruments or injections and then extracting the child, etc. See the difference? There is an issue of intent here that is very important.
There is also the case of ectopic pregnancy, where an embryo implants in the fallopian tube and begins to grow there, which will eventually rupture the tube, potentially killing both mother and child. In this instance, the tube may be removed (with child inside), and yes the child will die, but again the intent here is to save the life of the mother, not to kill the child. If there were a way to replant the child in the womb or save it somehow this would be the best option, but because we aren't there technologically, the unfortunate and unintended side effect is the death of a child. This, however, is NOT an abortion, because the aim is not to kill the child. There are ways to kill the child (and thus save the tube) but this would be a form of abortion, because the intent would be to kill the child directly. This concept is what we call the principle of double effect. More on that
here.
In the case mentioned, the first doctors the mother went to see said the girl was in no immediate danger and therefore would not do an abortion. So she went looking until she found docs that would. I can understand her duress and worry for her child, but directly killing both her grandchildren was not the answer, now the poor child will have to deal with this as well growing up. They could have watched the girl, made sure she was not in immediate danger, let the babies reach a gestational age where they are viable outside the womb if possible and then deliver them. (I believe she was already close to 5 months along anyway.) If there was danger to the girl, they could have delivered them early and done their best to save all 3 lives, rather than kill 2 of them directly and intentionally.
Also on the subject, why are Catholics automatically excommunicated for having or participating in an abortion, but not for other sins (like rape or murder)?
Mostly because there is still a recognition in our culture that murder and rape and many other sins, in general, are wrong. We don't have pro-murder or pro-rape rallies, or legislation trying to protect people who want to rape and murder. When the culture around us starts to try and re-write natural law, the Church steps up her reminders that, NO, no matter what our culture says, abortion is not ok, and the automatic excommunications are a reminder of the severity and grave immorality of abortion in a world that is trying to convince everyone it's ok. It's also because of the frequency and sheer grandeur of the problem, millions of children are being killed worldwide, likely more than other murders and rapes put together. It's a kind of prioritizing, the Church puts such severe canonical penalties on the act because it is such a huge problem, one of the biggest of our day. If this problem were to subside, and another to take its place, the discipline would likely change to reflect that, since this is just a disciplinary matter, something that could change if the moral climate ever changed.