Rear End Movement…

Ok so I was rocking the bike back and forth and felt movement through the foot pegs. I am pretty sure one of my front wheel bearings needs to be done, but I am kind of concerned about the rear end. I had my wife grab the handlebars and rock the bike side to side, when she did this, the axle was moving kind of up and down to the rear housing (see circled spot in pic), it was definitely a bit wiggly. What is the problem (can’t be normal for any movement I would think) and what do I need to do to fix it?

As always, any help is greatly appreciated.

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