What is the verb of 要回过头来走老一辈的路?
"回过头来走" should be interpreted as 回(过)头 - 来 - 走. Then

回头 - turn round
来 - to
走 - go/follow


过 is used for denoting the completeness status.


  用在动词后,表示完毕。如:吃过(吃完);起过(已经起床完毕)


Your understanding of the whole sentence is correct; but you lost the meaning of "回过头来" (turn round backward). 奏月's father is confusing; his daughter has graduated from college and could engage in some modern, advanced or easy job definitely. But she still decided to take tofu making as the work, even it's old, and hard.