If you can't get the spindle out (to be clear by the spindle I mean the main axle going through the rear wheel) then that itself is an issue. It's either seized on to something or a bearing has collapsed in the wheel or sprocket carrier.
The way I've got seized spindles out before is plusgas, leave a while and then place a block of wood against the end of the spindle before beating it with a 4lb hammer.
Once the spindle is removed that entire chain adjuster block just slides out.
For Clarity
Remove the spindle marked by red arrow
Slide out adjuster marked by yellow arrow
