More information is needed. However, speaking in general terms, when her passport is scanned upon entry into the United States, assuming the bench warrant had been entered into LEIN/NCIC system, it will "hit". Depending on the seriousness of the charge behind the bench warrant, location of the issuing court, she may be taken into custody for arraignment on the bench warrant.
If the arresting jurisdiction doesn't want to pick her up, she might be denied entry to the country. You need to consult with an experienced state/federal criminal defense attorney to deal with the outstanding warrant in the local court and at the same time attempt to arrange your relative's entry into this country to accomplish that task.
Please understand this is a general answer for the benefit and entertainment of the public and no attorney client relationship is established. Questioner would need to retain answering counsel and provide him further facts or information before a knowingly accurate opinion can be given to this specific situation.
She will either be arrested due to the warrant or denied admission to the U.S.
This is general information and not legal advise. This communication does not create a lawyer-client relationship.
I recommend that you relative retain Counsel to work with the Court to allow her to come back. This would consist of the lawyer speaking with the Court and the Prosecutor to see if they will agree to dissolve the warrant to allow your relative to return to the United States and not be detained at the border. She will have to provide proof of her itinerary and a date certain on which she will appear and perhaps post more bond. I am sure that there is a way to resolve this matter so that she can get this all taken care of.