Gary,
Looking at the design of the machine with the new photos, I see a LOT of areas where the machine is not very rigid. This lack of rigidity is where you will get chatter.
1) As pointed out previously, the router mount is very weak, could be beefed up with gussets to join the horizontal and vertical parts.
2) long, un-supported round shafts (bearings appear to wrap all the way around the shafts). There is very little rigidity in these rails, introduce cutting vibrations and you got a "chatter box"
3) Poorly supported table. There is very little structure supporting the table and thus the part. I bet with very little pressure pushing down on that table, you can get it to deflect .010" to .020" easily.
Is the machine "junk", I don't think so. Can it work and do what you want, probably. Like any machine, you have to work within it's capabilities. In your case, lighter cuts, lower feed rates, and probably different cutters, for example; cutters with a helix flute as opposed to straight.
Chris D