My situation is somewhat different. My wife's mother was given no middle name, so making her given last name into a middle name was more a matter of adding the new name to the end of a short list. My wife was given her mother's maiden name as her middle name and her father's last name. She kept that name.
My children were given a unique first name but their mother's middle name and my last name. If my daughter chooses to maintain that tradition then the same middle name would exist through four generations through female ancestors. In principle the pattern could be maintained through female descendents much as a patrilineal last name is through male descendents.
Interesting. Was your wife's mother a foreigner? My wife is a foreigner and she has no middle name. We gave my son three names, which is the tradition in my family, and his last name is the same as mine, which is the tradition in my family, but neither his first or middle name is the same as mine. That's also a tradition in my family. (We don't do seconds and thirds, etc.) My wife's family also has a tradition of not doing seconds or thirds or naming people after other family members. It is her tradition not to change her name upon marriage, and neither she nor her sister nor her mother did this. My own extended family really doesn't have a tradition in this regard, although I think most of the females did change their names upon marrying. This is especially true if they married someone with an anglo-saxon name. If they married a slav or a dutchman or someone whose name was even weirder and harder to spell than ours, then they generally kept the original. One of my cousins married a Lakota man and changed her name to his: Running Horse. Very cool. I'd probably change my name to Running Horse as well.
My sister changed her name when she married her first husband, since he had an easy, one-syllable, four-letter English name and it appealed to her. She then kept that name even when she married a second husband. Her son, however, has the same last name as I do, which was her original last name before she got married. She also broke with tradition in another way, she gave him her middle name as a first name, and his middle name is my middle name, so she managed to name him after herself, myself, and our father in that way.