I know that abortion is permissible if physical health of the mother could be compromised, but what about the emotional health of the mother (or the father for that matter) - if a couple sees divorce as a very real option, could an abortion be permissible?
Getting divorced would NOT serve as any halachic basis for an abortion.
This is evident from the a Teshuvah in Choshen Mishpat (Siman 69) (Volume 7, page 300) of "Igros Moshe", where Rav Moshe Feinstein, zt"l, wrote that abortion is prohibited but didn't mention an exception for someone getting divorced. In that Teshuvah Rav Moshe wrote about how terrible abortion is and called it retzicha (murder) starting at 40 days (or 41 days), and certainly prohibited before, as well. Had there been any halachic basis for such an exception (such as exceptions made when the only way to save the mother's life is by doing so) he would have mentioned them. Rav Moshe explicitly states that the Tzitz Eliezer was incorrect with his leniencies regarding abortion based on the misinterpretation of the sources he used to support himself.
In very, very broad terms -- some authorities will allow an early abortion to prevent significant anguish. (There's an mp3 of Rabbi Yona Reiss mentioning this with regards to a pregnancy found to have severe developmental challenges, if we think it will destroy the lives of this couple, according to some opinions.)
While it's ideal for most children to be raised by a father and mother as a family, people can manage all sorts of things. As difficult as single parenting or joint custody can be, I don't think the average case of "this couple is divorcing" (assuming that there will be some sort of competent parental figure) approaches anywhere near the hardship that would cause some rabbis to allow an abortion -- or to put it better, it's a terribly difficult situation, but I don't see how [in the general case] an abortion would really fix it.