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. Life is something of the greatest value and should not be looked upon lightly at all.
It is exceedingly important that no one misinterpret halacha to try and "allow" for an abortion when it's forbidden (and a major sin). The baby - who is unable to speak and defend himself - is the true victim of abortion. Rabbi Moshe Feinstein, zt"l, wrote about how terrible abortion is and called it retzicha (murder) starting at 40 days (or 41 days), and certainly prohibited before, as well. Except under the most extreme situations (such as danger to the mother's life) it should be recognized that there is another individual who wants to live - the baby. In Choshen Mishpat (Siman 69) (Volume 7, page 300) of "Igros Moshe", 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.
Life is of the greatest value and the Torah demands it be treated as such. The organization E.F.R.A.T. in Israel (which, I believe, has helped saved over 50,000 lives) notes that none of the mothers who they helped ever regretted having their baby. In contrast, it is common for women who have abortions that are not permitted halachically to have a powerful and enduring sadness/depression. "ובחרת בחיים - למען תחיה אתה וזרעך" - "and you shall choose life - so that you and your descendants shall live" (Devarim: 30, 19). Whether or not you are in Israel, I'd recommend contacting EFRAT - http://www.friendsofefrat.org/.
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.