Penned by civil rights activist Oscar Brown Jr in 1963, "The Snake" tells the story of a woman who takes in a frozen snake she discovers on her way to work.
After reviving the creature, it retaliates, giving the woman a "vicious bite" and killing her. When she asks why, the creature replies that it is a snake, implying that it is in its nature to bite.
Mr Trump has long used the song as an allegory of immigration law to claim immigrants from Syria and other war torn nations might end up harming America.
The US leader routinely read the poem at events during the presidential campaign. He used it again in a speech to the Conservative Political Action Conference (CPAC) last week.
Brown Jr's, Africa Brown, told CNN that her father's words were "being stolen to promote his hate message and intolerance and it's absolutely wrong."
She said: "The elephant in the room is that Trump is the living embodiment of the snake that my father wrote about in that song,"
Her sister Maggie Brown also noted that the original premise of the poem was at total ideological loggerheads with Mr Trump’s anti-immigrant agenda.
"It's a political agenda that deals with separatism, racism, sexism, and it's kind of thing that's polar opposite to what Oscar Brown Jr was about and so, to actually quote his words verbatim every time, pulling it out of his breast pocket as if it's this coveted thing that makes him a rock star."
The daughters said they believed Mr Trump is stealing the poem from their late father, who passed away in 2005.
They added that they had sent cease-and desist letters but Mr Trump could claim he is not infringing copyright law by citing fair use.
Africa said if her father, a singer, songwriter, poet, activist and one-time member of the Communist Party was alive today, he would not agree with Mr Trump's political agenda.
She said: "He always worked with all people of colour. He was never against immigrants."
Mr Trump, she added, was "attacking people of brown colour and my father supported people all the time of all colour."
Five years after Brown wrote the song, it was released as a single released by American singer Al Wilson.
It was based on "The Farmer and the Viper” - one of Aesop's fables – and the moral premise was that you can inadvertently be the victim of your own kindness.
Mr Trump’s usage of the song has not just been criticised by Brown’s daughters.
After his CPAC speech, conservative communications and public affairs strategist Steve Schmidt said: “Trump’s snake story is vicious, disgraceful, utterly racist and profoundly Un-American.
“That this is how an American President speaks of immigration is a tragedy. This crowd of cheering extremists are the heirs of the Know-Nothing’s and nativists that have always plagued us.”
Others have speculated whether Mr Trump’s obsession with the poem comes from being able to relate and identify with the snake in the song in some way.
“Historians will view it as obvious that Trump was describing himself in ‘The Snake,’” Dan Lavoie, an aide to Democratic New York Attorney General Eric Schneiderman, said in February. “His over-the-top recitation will be the narrative device for the first big post-Trump documentary. And they’ll think we’re all so dumb for not recognising it in real-time.”
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