The conflicts and mistrust were, as I understand it, largely on the part of secular rulers and some Church conservatives; the Iberians fought the Jesuits for mission lands in South America, and some European rulers ended up distrusting the order.
But the Jesuits becoming their own church makes no sense. Ignatius of Loyola, the greatest counter-revolutionary of all time, set out to restore Catholicism in Europe and spread the Catholic gospel abroad; to separate from the Church is to be no better than Protestants.