Because I don't think it should be like it is in the picture. I can move it all around in the hub.
What you are describing is perfectly normal if the bearing parts are OK and if the race is not loose in the hub
The bearing cone is held stable when fitted onto the spindle, and the race is pressed into the hub. When the entire assembly is properly assembled and adjusted with the nut the taper of the cones holds them centered in the bearing cups
What to look for. The hub is machined for a "drive" press fit of the race. Clean it up, get the grease out, and see if there is any movement of the race. SOMEtimes the race wears a ? cavity ? in the hub and becomes loose
Examine the race for pitting, scratches, rust, odd wear, etc. Same with the bearing cone, examine the rollers by turning them, and looking as well as you can under them at the cone inner part.
Test the fit of the bearing cones on the spindle, and examine the spindle surfaces for wear and damage, including the seal lip surface. If that surface is worn badly, there is a product known as a "speedi sleeve" that is a very thin, precision sleeve, goes over the spindle to provide a "new" seal surface. I believe they are a trade name of C/R seals (Chicago Rawhide). They have been in business longer than any of us have been alive, and I'm 74
Then repack with a good grease and replace the seal. Be sure to put a little grease on the seal lip so it is not dry. No need to "pack" the entire hub cavity with a massive amount of grease
If you don't know how to adjust them, go to MyMopar and download a service manual there for free. You may have to get Dodge vs Plymouth manual depending on year