Man of the Family is the second book in the Little Britches series.
From the 2001 audio book:
Young "Little Britches" life is radically changed when his ailing father dies. Then his mother reveals a terrible secret and the family is forced to flee their Colorado ranch to an uncertain future.
Fortified with the Yankee ingenuity his father taught him, at age eleven Ralph takes on his new role as Man of the Family. His mother deplores her inability to give her children everything materially, and instead gives them much to build their lives and character upon.
Together Ralph and his mother face true unforgettable pioneering adventures in Littleton, Colorado. Young Ralph becomes a Cattle Drover foreman, and helps start a new family business. Then the adventures really begin....
Father and I Were Ranchers
The Home Ranch