The phrase 'insistence against' is correct and can be used in both spoken and written English
You can use it when you are emphasizing a strong resistance or opposition to something. For example, "My insistence against the proposed changes was ultimately unsuccessful."
At Dan's insistence, against the management's advice, he put me in a revue with him, Danny at the Palace.
Cross was a compelling character, but the book became Patterson's breakthrough because of his insistence, against all received opinion in publishing, that it should be advertised on TV.
Probably the most famous "fact" about Columbus — his insistence, against overwhelming scholastic opposition, that the world was round — was the work of a fabulist, Washington Irving, who wrote the first modern biography of the explorer.
But President Pervez Musharraf, who until last November was also chief of the armed forces, preferred to focus on developing conventional warfare, training and equipment to use against India.It was not until 2003 that Pakistani soldiers were at last deployed, at America's insistence, against the militants.
From 1999 there will be a $500 $4000 next year) per child tax credit, available even for couples earning as much as $110,000 a year and also partially refundable, at the Democrats' insistence, against payroll taxes for those too poor to pay income tax.
"Swindon Town appreciated Jonathan's position on the matter and, despite the manager's insistence, decided against fining the player.
Jawaharlal was also attracted by Gandhi's insistence on fighting against British rule of India without fear or hate.
The insistence on sanctions against Iran — effectively ignoring the Declaration of Tehran, and without even giving Iran time to respond to the comments of the "Vienna Group" (the U.S., France and Russia) — confirmed the opinions of many analysts who claimed that the traditional centers of power will not share gladly their privileged status.
On Theodora's insistence, and apparently against his own judgment, Justinian had Anastasius' nephews executed.
In the New York Times of September 17, 2009, Roger Cohen wrote concisely what I have advocated for many years: "I cannot see any deal that will not at some point trade controlled Iranian enrichment on its soil against insistence that Iran accept the vigorous inspections of the I.A.E.A.
In the embittered atmosphere caused by Clement's deceit Dante turned his argumentative powers against papal insistence on its superiority over the political ruler, that is, against the argument that the empire derived its political authority from the pope.
