Joe – Your washer was manufactured by Whirlpool and is essentially a re-badged "Duet Sport". There is 'Shop Manual' for this family of washers, and their Kenmore cousins, at:
This is a little slow to load so please be patient.
The symptoms you describe indicate a fractured spider and/or failed bearings. The repairs are the same in both cases. Renew the spider, bearings and seal.
The only warranty that appears in the manual for your machine available on this site at the first link below indicates that there is only the one-year warranty on all components.
Not like the Frigidaire built machine, which was discussed above.
The good news is that the spider for your machine is available separately, item 27 at the second link below. The bad news is that Whirlpool in their wisdom have decided that the front and rear sections of the outer drum have to be purchased together, items 8 & 21 in the second link below. From Whirlpool or Sears the bearings are not available separately but come already fitted to the rear section of the outer drum.
Defective suspension springs and/or shock absorbers may be responsible for some of your drum movement. The manual referenced above will indicate how to check these.
Should you feel that you could change the seal and bearings yourself without renewing the entire outer drum please let me know and we will delve further.