More Than Likely The Drum Mount Is Broke In The Back. This Is Common On These Machines. Gam Ahold Of One Edge Of The Drum As You Rotate It To Several Different Positions. If The Drum Mount Is Broke It Will Move To The Side In One Position But Not In The Other. The Drum Is Mounted On A Bracket On 3 Locations.
The "drum mount" referenced on Kenmore front-loaders - this "3-location" description - seems to indicate it's a "cage" bolted to the very back of the drum itself - a part INTERNAL to the entire drum assembly ... and isn't a D.I.Y. job. You'll likely need a new "tub-spin" assembly ... which costs more than a brand new, high-end washer after the technician labor kicks in. My former Kenmore (417.29042992) didn't show this "3-location" drum *holder* available as a separate piece ...
But ... before you throw too much money into a repair - and you *DO* realize that these modern, rather expensive washers / dryers *ARE* simply "throw-away" items, don't you? - check the level / shock absorbers - mounted at 5 and 7 o'clock on each lower side of the drum as you're facing the front door.
When one breaks - and many do - this throws the whole machine outta whack and that's generally the cause of the initial "banging" of a drum. Using the machine after that only leads to MORE damage - usually fatal to the machine as far as $$$. One banging? VERY bad. More bangings? Death of the machine is imminent.
A pair of shocks are 25-40 bucks - and an easy D.I.Y. job - and may allow you to extend the life of YOUR particular machine if something more serious hasn't already been destroyed - but you can never wash many unbalanced loads - i.e. VERY large, absorbent items such as a super-thick bath mat - inside the drum - EVER again. Once a drum has banged, it's a sign that it's gonna happen again ... and it'll be easier to happen than before and will continue to "eat" itself to death.
Good luck! Me and my new Samsung 328 with VRT (Vibration Reduction Technology) will say a prayer for both you and your older Kenmore ('cuz you're gonna need it!)