Thanks for the picture. I was envisioning a project pinned between two narrow stream banks. You have plenty of "elbow" room to operate, and that should make things much easier.

It looks like there is a fair bit of clay in your existing soils? (Although the eye is easily deceived.)

What type of sub-soil will exist at the base of the core trench? Has your contractor dug a few deep test trenches to sample the materials? It would literally take him 5 minutes with an excavator of any size.

I would create a sump (deep pool) at the upper end of your designed pond and intercept the running water at that point. Get a trash pump (or two) and a few hundred feet of lay-flat hose, and pump the stream water all of the way around your entire pond area plus the dam and core trench. Wet clay in a construction project always slows things down and increases your costs. This includes not only the core trench and dam, but any work in the pond basin itself.

Another option would be to excavate a trench just one bucket wide that goes around your entire pond area and re-connects to your stream bed well past the dam location. (Your eyeballs on the actual site should be able to determine with your contractor which option is easier.)

The core trench (and any other clay seals) needs to be built in 6" lifts of clay-rich material, wetted to the optimal moisture content, and then compacted (preferably with some type of padfoot roller). You then move on to the next lift and repeat the process

Does your pond bottom have enough clay content to seal after you scarify (till) and re-compact?

How deep will your pond be at full pool? If about 10' deep, then a 6" lift of clay compacted throughout the pond basin, plus another 6" lift spread over the first layer and compacted should be capable of sealing your pond.

All of that wood debris in the picture must NOT be included in any of the clay sealing areas! That wood will decay, and then leave voids in your dirt fills which can later turn into leaks.

I hope that helps a little bit more with your vision of the process.