Ok, this is a huge physics dump but I hope you can follow and understand it, as I also think it's quite interesting.
Tires are usually attached to the rims securely enough that they can handle quite a bit of sideways force without pulling off from the rims.
To explain what is going on, I need to delve a little bit into simple mechanics, but bear with me.
It's a complicated question HOW much you could turn the wheel and still keep the wheel undamaged. The traction forces are caused by static friction that breaks and re-forms very fast as the tire has very small slip angle. As you might know, static friction coefficient is usually slightly higher than kinetic friction coefficient - you can demonstrate this with any object on a table.
The mouse is a good example. As it rests on your desk, no sideways forces are applied to it. If you start lightly pushing the mouse with your fingertip you can feel the pressure your finger is exerting on the mouse. Your finger's point that touches the mouse is the contact patch, and the force to mouse is delivered with pressure on that contact patch, so you can directly feel the amount of force applied with your finger, making it a very good physics demonstration since anyone can do it with almost no equipment.
As you slowly increase the pressure, you'll notice the mouse does not immediately move. You have to increase the pressure against a certain point, and THEN the mouse starts to move and you'll probably notice that the pressure you feel with your finger reduces at this point.
This is because you have crossed over the static friction barrier, and the friction is now defined by kinetic friction coefficient which produces less resistance to movement than static friction coefficient. You'll notice a "notch", so to speak, a sharp reduction in the pressure between finger and mouse as the mouse "jumps" forward.
This is, incidentally, the reason why "drifting" in turns is always an inefficient way of doing things, because a slipping tire always produces less friction forces (acceleration, braking, or steering) than a wheel that is rolling on the surface with a static friction contact patch. In other words if you understeer or oversteer in a curve, you will not be able to go as fast through the bend as you could without any significant drift. There are some exceptions in low friction environments, such as gravel or snow compared to tarmac. If you look at WRC cars, you'll notice that they hardly ever drift on high friction events, because it reduces the cornering speeds. By comparison, on loose surfaces the WRC cars are actually sliding almost all the time, and instead of steering the cars through bends with the cornering force, they turn the car towards the inside of the corner and use the car's forward acceleration to produce centripetal acceleration.
In theory, this method of cornering is not as fast as static friction cornering. However in practice it usually produces better results on loose surface, as the vehicle can achieve positions not possible for straight steering, and moreover the driver has more control since they don't need to worry about the breaking point of static friction - they are continuously operating on kinetic friction so they're not worried about the abrupt shift from static friction to kinetic friction, which is what usually causes drivers to lose control of the vehicle at high speeds.
But, to return to the original point. How much sideways slipping can a tire take before it is damaged, pulled off the rim or otherwise?
It depends on tire structure, surface friction, speed, slip angle and duration of the slip.
Usually, tires are not pulled off the rims by sideways slipping. If you understood what I wrote before, you'll notice that the friction force is always at its greatest when the static friction breaks. When the object starts to slide on the surface, the force does not increase but instead decreases.
Let's vision a tricycle gear aircraft sitting on the tarmac. The pilot, being a noob, has turned the nose wheel 90 degrees around and is enthusiastically revving the engines, which are quite powerful indeed.
As the pilot increases throttle and wonders why the plane isn't moving - he has cleared parking brakes and removed choks - he is increasing the force that is applied to the tarmac through the contact patch between front tire and the surface. But the tire doesn't immediately start to screech forward on the tarmac, because there's static friction stopping it from moving.
When you increase the force pushing the aircraft forward, the stress between the tire and road increases, until at some point the static traction point is lost and the tire starts to move sideways on the tarmac. But, at this point, the friction force between tire and tarmac is
reduced, so the tire experiences
less sideways stress as it starts to move.
Therefore, if it wasn't pulled off the rim before that point it won't be pulled away after it starts to move.
Now, the secondary effects of dragging the tire across the tarmac start to affect things. Namely, you're dragging a rubber hunk on tarmac with a lot of weight on top of it. This causes a lot of kinetic friction, which causes a lot of physical wear on the tire surface, and a lot of heat. In other words, the front tire will fast develop a flat patch that gets deeper and deeper, and meanwhile the tire is also heating rapidly. The heating increases the amount of wear as the rubber gets softer. As the hapless pilot continues to speed away on the surface, the damage on the tire's surface gets deeper. At some point, all the rubber on the tire's surface is worn off, leaving a patch of the tire's weaved structure to be in direct contact with the road.
At this point, the friction between the road and tire usually drops off sharply because canvas and steel are not as "grippy" as vulcanized rubber. But it doesn't stop damage from occurring - the nose gear just slides a bit easier from this point on.
After some time of sliding on the "naked" tire, the structure of the tire will fail and it will deflate. So now the aircraft starts to slip on the nose gear rim, as the torn wheel usually rips off from the rim at this point. This is metal-tarmac friction, not very significant in force but the heat will be incredible and sparks will be flying, and the pilot will finally realize something is rather wrong as the aircraft's vibrations will sharply increase (an underestimation of the century, but whatever).
Of course this is assuming that the landing gear doesn't collapse due to unintended prolonged "dragging" before this point. Usually they're designed to be pretty sturdy, but I have no idea about the specific tolerances of P-38 landing gear for example.
This example also assumes that the tire is already at 90 degrees slip angle when it starts moving. In your example, the aircraft would be rolling when the tire would be turned. In that example it's hard to know what exactly would happen. It would depend on the speed you're rolling at, and how fast you turn the nose wheel around.
What would happen in real life is that as you start to turn the nose wheel, the slip angle suddenly increases, and the nose of your plane will start to turn into that direction as the tire wants to keep rolling on the surface instead of sliding. As you increase the tire's angle, the aircraft is turning faster and faster, until at some point (and this depends on your speed) it will either break its traction again and start sliding (at which point your aircraft stops moving in an arc and starts moving more or less forward although it may still be rotating), and after this point it doesn't really matter if you turn the tire to full 90 degrees deflection or keep it at that critical angle. Your aircraft will likely also start to slow down at this point because of the nose gear friction. If you keep the tire at the critical angle, the aircraft will slow down and attain grip at some point again, starting to turn your plane nicely again. If you turn the nose gear to full deflection, then I suppose your plane would just skid to a halt.
I hope you could follow all that, and the important thing is - the sideways force of traction or friction itself is unlikely to damage the tire. Landing gear collapse due to sideways stress is more likely, but the tire itself will probably be able to take the punishment - for a while. It will fail due to wear and heat in an extended slide, but not immediately.
Here is a video of a situation where an airliner had to land with nose gear turned 90 degrees due to mechanical failure. You'll notice that the tire doesn't immediately fail, but a lot of white smoke is generated, then when the tire deflates its remains are torn off from the rim and the metal comes into contact with the runway.
Jet Blue Airliner, KLAX, 9/22/05Jet Blue Airways Flight 292 (wikipedia article of the incident)
By the way, all aircraft have specified slip angle limits which, crucially, come into play in crosswind landings. The landing gear is designed to tolerate certain amount of sideways stress as the tires come to contact with runway at an angle. This critical angle determines whether the aircraft can safely land at any specific crosswind or not.