Am I allowed to take my wife to chutz laaretz on holiday for shalom bayis purposes?
Yes. Although only three reasons are mentioned by Chazal for which it is permitted to go to chutz la’aretz (getting married, making an income, and learning Torah), poskim write that it is permitted to do so for a variety of additional mitzvos (Rambam already mentions honoring parents, which is not mentioned by Chazal). This is the reason for which we find many prominent rabbis going to chutz la’aretz, even for the purpose of a holiday, because they feel that this is necessary for their health, or for visiting graves of tzaddikim (some do not consider this a mitzvah), and so on.
There is no doubt that shalom bayis is a great mitzvah–Shabbos candles take precedence over Chanukah candles for this reason–and if the Torah permits erasing the Name of Hashem for its sake, it is certainly permitted to go to chutz la’aretz for it.