'insisted her' is correct and can be used in written English.
This phrase can be used when one person insists, or demands, that another person do or believe something. Example: John insisted her to go to the movies with him.
She insisted her supporters not indulge in triumphalism.
But he insisted her triumph was fully deserved.
His mother insisted her children work hard at school.
She insisted her son be tutored at home.
Mrs. Wang insisted her husband would turn up someday.
She insisted her action had not aimed to provoke.
At home, she insisted, her goal is not "to sour the story of Normandy".
Ms. Safi said her observers counted 2,850 votes — but insisted her opponent had even less.
(The Jaguar is gone; Ms. Wilson insisted her husband sell it when they moved).
After they divorced, Mrs. Flynn switched back to her maiden name and insisted her children follow suit.
Ms Bernhardsson insisted her "completely apolitical" group would work with authorities and hit out at "censorship" and criticism on Facebook.
