Chevy Avalanche 4X4 problems

I have a 2003 Chevy Avalanche 1500 with 78,000 miles on it. Lately when I put the powertrain into four wheel drive ( either the auto 4X4 or 4-Hi or Lo)it becomes hard to control the steering. She jumps to the left or the right, back and forth sometimes. This is alot more noticable under hard acceleration when she will pull mostly to the right. I have put larger more aggressive tread tires on (33 inch) and also installed a leveling kit this past summer. A mechanic at a local GM dealership said this is happening due to the larger tires, but other owners that have put larger tires on do not have this problem. During my last oil change, the service attendant said my front drive lubricant was a bit dirty, not bad, but I should think about changing it. Any suggestions.

It’s the monster tires. Because you have so much rotating mass on the axles now, and it’s so far out from the axis of rotation, the engine and other forces are via the massive tires overwhelming your ability to steer. The tires are acting like huge gyroscopes.

Try adding steering stabilizers. That dampens the effects of the forces and may bring it under control.

Then why is handling not different when it is in two wheel drive? It just handles as it always has when in two wheel drive.

You MAY have a front diff problem.