It's a silly episode, but really underlies the role of women in the 19th century. Women had very little opportunities outside the home and, if a husband chose to leave her, could only hope to find another husband or be destitute.
Some of it was rather foolish - Caroline and Charles have had minor spats in the past, but Caroline would not have left him over this issue. Laura leaving Almanzo just to support her mother is also stretching it.
While it's a funny episode to watch, it's important to remember what exactly the women were fighting for, in an era where they were not even allowed a vote.