A parking gear is a gearbox lockup, and is far more secure than your "parking brake," which is just a primitive, mechanically-levered shoe-brake. A certain amount of roll or play is to be expected in any automatic parking gear, but if it the vehicle never becomes truly secure (the gear is not properly engaged) then something is very wrong with your transmission.
You don't mention how many miles on the car, but if it's a lot, then the normal amount of "play" will be increased because of wear on the mechanism. You can use the emergency brake (the proper term for the handbrake) to eliminate the play between the moment you stop and the parking gear engages - but if you're convinced the parking gear is not properly engaged, you should really get this checked out by someone confident in his or her ability to assess the situation.
Here's a link that explains a parking gear: http://www.howstuffworks.com/automatic-transmission5.htm
(Operators of manual transmissions sometimes use the hand brake for parking, but usually leaving the car in first or reverse is more than enough. It's useful, however, when the car is idling in neutral.)
(The term "parking brake" is a misnomer. No doubt your state inspectors and motor vehicle officers refer to it as the "emergency brake." It's true purpose is to be available at unlikely moment when the hydraulic brakes fail. And believe me, they are no substitute for real brakes, either.)
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David \\ (98 S70 T5SE Black, misc mods (mostly lighting), red calipers) (92 940GLE)
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