Bike rack wobbling
 

I got a Yakima rear bike rack that I attached to my tow hitch. Took it out on the road with a bike but It seems to wobble quite a bit, but be fine. I've never had a tow hitch let alone put anything on it so not sure if this is normal.

Tighten the bolt.

While I don’t have a hitch on my Q7 a hitch is a hitch and my bike rack on my Ranger wobbles a lot more than I’d like but I guess it doesn’t hurt anything.

For light stuff on your hitch, you can use one of .

I have a Thule Apex bike rack. When installing it, you have to make sure that Auto pin goes in the hole on the side of the receiver and once it's secured in the hole, you tighten the locking knob to the point where the carrier is nice and tight. The only wobble you will get at this point is from the actual bike rack and bicycles, which is noticeable, but fairly light. Your connection between the carrier and receiver should be rock solid.

The pin was in and we tightened, but there was still some wobble on the connection. I don't think it's going to fall out. My fear is it puts too much stress on the hitch.

The hitch can handle 770 pounds of weight and tow 7700 pounds.... the wobble on the bike rack, even fully loaded with bikes, is inconsequential as far as the hitch is concerned. However, it sucks to look at the wobble!
As an aside. this is another thing I really like about the 1UpUSA racks (https://www.1up-usa.com/product-category/bike-racks/) - rather than a hitch pin they have an expansion mechanism that provides pressure within the hitch receiver to hold the rack in place, and that keeps it from wobbling at all. I've gone on pretty rough roads/trails in Southern Utah to get to trailheads with 4 bikes on the rack without worrying about the rack itself. Unfortunately, the system is pricey so for people who don't use it often it is probably not worth it.

Ditto for Thule.

If I have 40 lb hitch and with 4 bikes it could be nearly 200lb, and I fear going over a fast bump could easily cause triple the downward pressure with the wobble

OK, but that's not how max tongue load works. Needless to say, you won't overload your hitch with 200lbs and some bumps, unless of course you drop it off the cliff, but in this scenario you have other problems to worry about.