While studying IATIJ Revised I came across むしろ and かえって. I did not feel that it had a good explanation so I decided to look at other texts and even on this site. While neither are listed on this site in the grammar library I feel that someone might have the same question in the future. I found a better explanation of かえって in Tobira and in A dictionary of Intermediate Japanese Grammar. The only place I could find a different explanation for むしろ was in A dictionary of Advanced Japanese Grammar. I then asked my Japanese wife for an explanation between the two and this is a summation of all of the textbooks and my wife's input. I would really like these to become grammar points on this site if at all possible.
むしろ： This is used to suggest rather, preferable, or more than ~ when two options are available. It is often paired with the 方が～より combination.
eg. 1) 日本語を読むよりもむしろ話すのが好きだ。 I (would rather speak/ prefer speaking) Japanese than to read it.
かえって：This has a very similar meaning to むしろ but differs in its nuance. This means rather but with the connotation of "in contrary to one's expectation."
eg. 2) 今年の3月よりもかえって2月の方が暖かった。 February was warmer than March (and this is against my expectations.)
In eg. 2 you can replace かえって with むしろ but the meaning changes from being about going against expectations to just stating the facts.
You cannot replace むしろ with かえって in eg. 1 as it is your opinion therefor you cannot go against your own expectations.
I hope this explanation will suffice for all that are reading this and I will be happy to help if you have any questions.
