I had a slight wobble, but the Yakima Holdup comes with a tensioner/anti rattle pin that tightens the receiver to the rack. I use these on all my trailers and on my bike rack attached to my off road trailer too.. they work great.
Anti-Rattle Trailer Hitch Receiver Lock for 1-1/4" Hitches - 2-3/8" Span
Item # 63147
If your question is does my hitch attached to the car wobble, it did on my original car, but the one I have now doesnt wobble at all..