Checking for a bent rim
 

So I've had a mild shake while driving at speeds. Previously caused minor steering wheel shimmy and now causes a mild vibration (having rotated wheels front to back).

My question is this, does putting the car in neutral mean I can spin each tire freely? I would need to buy a Fowler gauge and arm, but I'm wondering if the AWD prevents me spinning the tires because the differentials might need to be spinning to work or? Also, would you check for bent rim at home or always have a shop do it? I'm kind of a starving student atm so trying to avoid expensive shop fees and "oh you need to buy a new rim" mechanics...

I'd like to fine the bent rim and put my spare rim in rotation, after removing the odd tire from it and installing 4 new tires I just bought. I'll then put the old spare tire on the bent rim for my spare.

Thanks