It's not there. You cannot show me it is there. Sorry but it is from a letter written to a church. Everyone knows this.
Actually I think it was Hugo Black that resurrected Jefferson's 'wall of separation' as he expressed it in his letter to the Danbury Baptists. Black, as so many secularists are wont to do, misused the phrase in his comments on Emersen v the Board of Education (1947). There is an excellent discussion of that here:
The Mythical "Wall of Separation": How a Misused Metaphor Changed Church–State Law, Policy, and Discourse
The Mythical "Wall of Separation": How a Misused Metaphor Changed Church
In any case you are absolutely right that there was no intent of the Founders and there was nothing written in the Constition to prevent intermingling of religion and government. There was intent clearly expressed that government should not have any jurisdiction over religion and the Church shall have no jurisdiction in government. Otherwise the intent was that government and religion coexist peacefully and productively.