2mm at the rim means a few hundred microns clearance in the bearings. This is 'a lot' and whilst it might just mean the bearing has gone out of adjustment, it is also quite likely that all is not well inside. If hubs are run this slack then it often causes damage to the seals, but if the seal lips ran dry, they could have worn, let water into the hub, and this caused the bearing wear. All rather chicken and eggish.
Cup and cone hubs are designed to be overhauled, so you should overhaul this one.
When you are done, the correct adjustment is a little free play in the bearing which just disappears when the QR is used to secure the wheel in the frame.
cheers