Well, Dooleysm, looks like you have a solution and don't recognize it. Rebuild the dam where it is, let the tree roots cause a leak and wash away the stuff your neighbor has that you do not want to see.
Now on a more serious note. What we have done in the past with a similar problem is to move the dam up hill a little. Dig out the pond to get some depth. You can use the dirt from the old dam to help with building a new one, just be careful not to kill the trees. If you go 15 or 20 feet from the old dam, that will probably be sufficient.