Helga Estby walked that distance in an effort to save her farm, an effort which turned out to be futile. If Helga had stayed home instead, she might have noticed something was wrong with the children and they perhaps could have received medical attention. The farm would have been lost either way, but perhaps the children would have lived.
I believe that money can't buy happiness. Helga Estby found this out the hard way and unfortunately for her and her family the money that was promised never came about. She would have been better off staying at home taking care of her family. Surely there was something that she could of done to earn money in her area. Leaving her family and heading towards New York was the worst choice she could of made.
Seeing as her walk was an incredible feat that no doubt forged the woman she would become, Helga Estby's walk to New York from Washington obviously would have been much different had she not made the trip. Her two children who died on the trip may have survived, of course, and no doubt things would have taken a completely different direction had she not, either good or bad.
She needed to do something to save her children and when the opportunity came up she took it. I do think though, that is was the journey itself rather than their eventual arrival that changed their lives the most. The children especially learned more about the world than they ever would have in school.