What year is the 250R? I think if the axle really moves a lot, it could either be the bearings, or the chain tensioners or both. If the chain tensioner bolts get striped, the rear end will move a LOT. I would be sure to check the chain tensioners on both sides. They are fairly inexpensive to buy, and you can get them on ebay.
THE 80's RAGE! Currently owns:
81, 85 Yamaha Tri Moto 125
83 Yamaha Tri Moto 200 x2
82,83 Yamaha Tri Moto 175 project
85 Yamaha Tri Z 250
84 Kawasaki Tecate 250
84 Honda ATC 70
85 Honda ATC 350X
84 Honda ATC 250R
(2) 84 Honda ATC 200x
82, 83 Honda ATC 185s
81 ATC 200
Lots of other parts and bikes