strong vibration at 70 mph

yeah so we have a 2002 chevy avalanche with about 110000 miles on it so its been through a lot =)
but whenever we get to about 70 mph to 76 mph there is a strong vibration in the truck .
we were changing the rotors and we noticed that when you pull on the right side of the wheel it actualy moves maybe half and inch like u were turning the steering wheel ... and the same when u pull on the left side it moves easily as if somthing is lose. we dont feel like takeng it to a dealer and pay around $200 just for them to look at it so i figured i would ask on here. we think it has something to do with the steering arm or somthing in that area
 
thanks

My 2003 Tahoe had the same problem... when i took it to the dealer they said it was something to do with a part of the steering arm and they had a recall on very few of the GM trucks and suv's with that problem... also like you mentioned check the braking system... my wifes cadillac cts was having a strong shaking or vibration at high speeds... and the brake drums needed to be re-surfaced... and that fixed the problem...