You can't hook up a DVD player through a VCR, period. And the PS2 with a DVD movie in it is a DVD player (which is why it does it "only when you watch DVDs", since games have no Macrovision protection on the outgoing signal). The only way to watch movies on any system (PS2, DVD player, whatever) is to hook it directly to the TV/Reciever, it can't run through anything that even has the remote possibility of recording the incoming signal, regardless of your intentions.
There is no workaround.
My suggestion would be to buy a switchbox for your reciever, since I'm guessing it has only a single input. Connect both the VCR and PS2 to this switchbox, with the switchbox's outputs going to the TV/reciever. Then just switch back and forth depending on which one you want to use at a given time. I have my GameCube and VCR running through a switchbox (ran out of connections on the back of the reciever, so they share one). But I have nothing running into the VCR.
What kind of reciever do you have? Any reciever capable of supporting 5.1 audio (since you mentioned surround) should have more than one input on it... Can't you just run the PS2 into one input and the VCR into another?