So far, I've found this concept can apply equally to fathers as well, not just mothers. Living vicariously through others isn't even relegated exclusively to a parent-child relationship, either.

My father ended up a doctor, even though his dream was to become an architect, and it all happened because his father (who was an architect himself) pushed/forced him to study medicine. He then turned to alcohol to manage and cope, and it went very well (/s).

I've always been artistically inclined, but my family had no faith in my capacity for creativity. As such, I've been dragged through the sciences until I was old enough to decide for myself. It wasn't just my mother (dad was out of the picture by this time), my maternal grandparents were actually the dominant voices in determining what I did and didn't study. I don't regret having studied a multitude of different subjects because I tried to make the best of it, but I do feel that I've missed out on some very helpful starter things in terms of creativity. Not to mention the deficit of self-confidence this ultimately generated, having been told repeatedly that my decisions and desires were stupid as I was discovering/developing them.