What you're experiencing is the copy protection on the DVD's.
The MacroVision Copy Protection is effecting the VHS deck as it should. It does that to deter you making copies onto VHS tape from the DVD (because it's highly annoying to watch a movie like that, right?). But the manner in which it accomplishes that also effects the video output of the VHS deck when you're using the VHS deck's video out.
Don't run the DVD player through the VHS deck is the best way to solve it.
If you must run the DVD player through the VHS deck you can either modify the DVD player to not ever activate the MacroVision circuit (usually not easy if it's even possible with your particular player). Or you can go to Ratshack and pick up an RF Modulator to be installed between the DVD Player & the VHS deck.
It should be noted that the RF Modulator does not completely disable the MacroVision signal. As the strangth of the MacroVision signal varies depending on which studio produced/distributed the DVD the RF Modulator might still let some of the MacroVision signal through. Disney is one of the studios that has the MacroVision signal sent out very strong and it's likely that their DVD's will still be distorted when played back through a RF Modulator & VHS setup.
