If your toe in (alignment) is out significantly it would do this too. But no idea why it would act up when you had the tires rotated. A separating tire can certainly make it pull one way, but won't usually pull one way and then the other. Unless the mechanic who rotated the tires dropped your truck off the hoist!!
I'd just bite the bullet and take it to a good alignment shop. That's their business, making it track in a straight line and handle well. They'll check all the front end parts too.