Leenia, the sequel song says the mother "lived alone without a man to share her life" so no she didn't remarry - according to Kushner's song.(Goodman said someone told him the story, that it is about a real person, and that she had eventually remarried. But let's look at it just as a song, is it a believeable fiction?) Presumably Penny had to work and probably the family wouldn't have been well off. They already had a piano and Penny could have taught the girls a bit of music herself. I agree that when I hear the words of the original song, I think to myself, "can she really afford not to use the government support; and also doesn't she and her children deserve to have it?" But that doesn't for me take away from the song, which I do find believeable.

[also there is nothing in the song to tell us how long, how many months, Penny held out after she fkirst took her stance)

I don't know the full circumstances of your niece, Leenia, so I can't comment on her decision. Maybe the boys will be glad to have a fund when they reach adulthood.