Bill:
Like Cecil said, visqueen won't last long term, if you go that route, you'd be better off using a pond liner type material, EPDM. IIRC they make it up to 40 mil thick.
I haven't done business with this company, but I'm posting the link so you can get an idea of the sizes of liners available.
http://www.justliners.com/epdm.htm The NRCS office 2 counties over do something like you are describing with ponds that are in sandy soil that leak. They dig down as far as they can, all around the pond, and drop a curtain of plastic down, sealing the seams. They say that it won't seal the pond completely, but it sure slows down the leak. Here, you can dig down 40+' and still be in sand, so yes, the water will hit the liner, go down and go under the liner.
From what you are describing, I think when your pond hits a higher level the water hits the old creek bed/sandy soil and seeps thru the soil and goes under the core trench in the dam.
I'm not 100% sure that the new core trench/liner sheet will stop the leak. If it doesn't go all the way down to watertight soil, I think the water could leak out around the ends or beneath the liner material.
