Thats incorrect. I found out that she is more likely to qualify for asylum under "membership in a particular social group" due to her relationship with her U.S. citizen daughter.
True, the "nationality" category in the context of asylum generally refers to persecution based on belonging to a specific nation or national group, not simply by having a relationship with a citizen of another country.
The concept of "membership in a particular social group" is used in asylum cases to cover specific situations where persecution is related to belonging to a group that shares a common characteristic that is recognizable and particular. In this case, being the parent of a U.S. citizen can be considered as membership in a particular social group.
She just has to say,
"Officer, I am seeking asylum because my family and I have faced severe persecution due to my daughter's U.S. citizenship. In my country, being the parent of a U.S. citizen places us in a socially distinct group that is targeted by criminal elements who believe we have access to wealth or U.S. government protection.
We have received numerous threats explicitly stating that harm will come to us unless we pay extortion fees, which we cannot afford. These threats are directed at us solely because my daughter is a U.S. citizen, which makes us a target."