There are several times when Nels and Harriet Oleson look as though they might be headed for divorce, and temporarily separate. Usually at the heart of the situation is how abusive and unkind Harriet is towards Nels and when he gets fed up enough with it, he ends up leaving.
In one episode, Family Quarrel, Nels moved out and moved into the hotel, leaving Harriet to live in the Mercantile with Nellie and Willie.
In another episode, Second Spring, Nels becomes fed up with Harriet again and decides he is going to become a travelling peddler and outfits a wagon to sell goods on the road. While doing this, he meets Molly, who owns a boarding house Nels is staying at. But of course, to complicate the situation, when Molly and Nels are about to kiss, Charles Ingalls walks into the boarding house and Nels reveals he is married.
Ultimately, even though Nels and Harriet to do separate several times on the show, each time they do decide that they love each other and decide to stay together. For the duration of the show at least, Nels and Harriet do not get divorced.
