Going through this bike and taking the chain and rear tire off I noticed a lot of side to side movement in between whatever the sprocket is bolted to and the hub.  No movement forward/back along the sprocket axis but where you can see the gap there's side to side play.

Is this normal, can I fix it, do I need to start sourcing a new back wheel?

I searched parts diagrams and they show a damper but other than that there isn't much info when searching it. 

Knowing what bike would help others to help you...

CT2?

Is the large snap ring still there? 

Hi B,
I am currently experiencing the same thing on my CT1C. I was lucky enough to find a NOS cush hub assembly. I also put a new big cir clip on it also and it really helped. It is better than it was but still has a little bit of movement. I have read that some side play is normal but back and forth is so not good.
Disclaimer: I am not a mechanic but just expressing my experience with this issue.
The great thing about this forum is the 2nd and 3rd opinions, agreements and disagreements.
You are bound to get a enough information to make a good decision about what you want to do.
Best forum ever.

Also the MX wheels of the same era have the sprockets mounted directly to the hubs so that may be an option.

Re the big circlip/snap ring, I think that Enduronut posted some time ago about the right and wrong way to fit these (I think that one side may have a bevelled edge). However, me being me, I can't remember which was the right way! 

Please forgive me if I imagined all of the above! 

Sharp edge would go out. 

 

I also moved the clip around 180 from the its original location and it seemed to tighten it up even more. I think the aluminum against the steel snap ring may wear a bit in places on the hub. Good to know about the beveled edge. Need to check that..

Sorry yes it is a CT2.  I can see the large snap ring it is still there.

Bike is a new project and only thing left is a new rear tire to take a test ride and noticed this.  Also the missing shock bolt