This means the mothers belonging to the same family - each brother's wife, the grandmothers, etc. all related.

Возможно, но я с трудом представляю что-то, не связанное с детьми, что делают именно матери, а не женщины вообще.
Поэтому "матери в СЕМЬЕ" по-русски звучит странно.

Every Thanksgiving, we go to Pennsylvania to spend it with my grandparents and most of my immediate family. On Thanksgiving day, while the men watch football on tv, the mothers of the family busy themselves with Thanksgiving dinner in the kitchen.

Although “mothers of the family” makes sense, I would have opted for “women of the family” if I was writing this.

That was exactly my point. There can be women in the family that don't have children.

Absolutely, that would be my logic. Nevertheless, “mothers of the family” would make perfect sense too.