If everywhere you dig, you come up with water-bearing subsoils, then you might need to switch your design (and thinking) to a groundwater pond.
It will be difficult to seal up any sandy horizons in your pond basin with a clay seal if you can never create a dry pond basin.
Can you dig a test trench at a couple of spots inside of the boundaries of your new pond design dimensions? Looking at your mixture of sand and clay, they should probably fill with water rather quickly.
Do you have the means to shoot a level between two water-filled pits? If they have the same level the next morning, then you are probably on a regional aquifer. If that is correct, and you have several sandy horizons, then I doubt you can pump your pond basin dry without serious pump horsepower.
However, that does potentially make your pond project much easier. I expect the overnight water elevation will be significantly lower than the water elevation you designed for after damming the stream? Is it a water level you can accept, based on aesthetics like your wife's view from the deck?
If your subsoils are well-connected to the regional aquifer, now you simply need to excavate a pond basin to create your pond. This will create a LOT of spoils! Do you have a place on the property to spread your spoils? It does not need to be flat over a large area. It is usually easier to build some attractive berms or other landscaping nearer to the pond to limit your costs in just transporting sub-soils.
I don't mean to throw a curveball into your plans. However, your local soil geology may have thrown that curveball, and you will need to build a pond that matches what the ground gives you. I hope my additional information above makes sense. Keep talking to the local contractor such that what he says to you makes sense, since he should have already dealt with similar situations if he has constructed many ponds in the area. Local knowledge is almost always more valuable than "internet" knowledge!
