My 10 Grand Am rear wheels are locking up in drive..they will turn in reverse

There's something seriously wrong in the transfer case or controls. It seems the rear driveshaft is locked up, and the front wheels are driving. The driver's side rear tire is skidding because it's trying to turn backward - rear passenger rear tire is going forward and rear differential has no option but to turn the driver tire in reverse (driveshaft locked). DON'T TRY TO DRIVE IT. Get it checked out and fixed.

I know what they did!, and the only thing you can do is take it back to the dealer. They have put in a different diff ratio. jack up one side of your car with 4X4 rotate your wheels your front diff goes 5 revolutions and your rear may turn 4 or 6 turns, when your wheels turn at different rates it increases the load on your drive line, if your wheels don't slip you must break something

ask the dealers what ratio was put in the rear diff
sound like the incorrect ratio against the front differential is used

Try this if rear drum brakes.Go in reverse about 8 feet and hit the brakes.This will self adjust the rear brakes and possibly fix the issue.Your rear brakes may have become locked.

Unless you have a positraction rear differential, I'm surprised that even three are turning! Four wheel drive is really two wheel drive because both differentials are "open" type. In an open diff, only one wheel has power at any given time. With a positraction, or "limited slip" rear diff, both rear wheels push with fairly even force but the outer wheel is allowed to slip when going around turns. Only true four wheelers have either a limited slip on both ends or "locked" units but it is impossible or really difficult to drive anything like that on the street. If you hold the left front wheel from turning unless the locking unit is broken, the right front should turn.

It sounds more like your rear end has a bad bearing or a bad pinion gear. If it has high miles it may be time for a rebuild. It could be brake related also, take off the back drum and see if anything is rattling around in there or broken. If your not hitting the brakes they shouldn't engage.

The short answer is "no", but working out why could be a little bit difficult. Any further diagnosis should be performed on a hoist or with all 4 wheels off the ground and the transfer box in 4H. Be aware that any of the following checks where front and rear wheels may turn at different speeds will generate an ABS error code and a light on the dash that may need a Dealer to turn off - if you have ABS. You'll also need a couple of hydraulic brake line locking clamps. The first check would be to make sure the front prop shaft turns in reverse as it does in forwards 4WD. Why it wouldn't, I couldn't tell you!
Stop the engine, and while someone is holding their foot on the brake, clamp off both front hydraulic lines to each of the front calipers. Release the hand brake (park brake) and release the foot from the brake pedal (keep foot off brakes from now on) and restart the engine (in nuetral or N), and whilst the engine is idling, select 1st and slowly let the clutch out (if it's a manual), or select D (if it's an auto). If the line locks are holding the pressure in the front brakes, then the manual should stall, and the auto's back wheels shouldn't be turning (but the engine would feel like it's in gear). That would confirm that the front wheels are driving when in forwards 4WD.
Then we do the same test but going backwards, so select reverse and let the clutch out (or R if auto), and if what you say is true, then the back wheels should be spinning away at idle. If the engine stalled, or the back wheels aren't turning, then everything is OK.
Remember to remove the line locking clamps after this test.
I would think that you may have only seen the wheel that wasn't turning when going backwards. These cars have open diffs - so the wheel with the most resistance to rotating won't turn, but the one on the other side will. This is the same for both the front axle and rear axle for most Grand Vitaras. Very few have a factory rear LSD, and I don't think any got a front LSD.
I've just had inspiration - if the front wheels don't drive ONLY in reverse 4WD, the only thing wrong would have to be the front diff engaging mechanism or its related wiring/switching controls. If the relays that control the pump that supplies air pressure to the diff engaging diaphragm in the front diff housing don't get the "I'm in 4WD" signal from the transfer box, the pressure is relieved to the diff and you're back into 2WD. My next check would be to see if your reverse lights are working when in reverse. See if your reverse lights come on when in 4WD or 2WD. If they aren't working, or coming on at the wrong time, then SOMEHOW, the wiring/plugs on the gearbox/transfer case may have been mixed up (during a clutch replacement?) or the wiring somewhere else is wrong. I would probably do the checking of reverse lights before the first test above. Good luck. Let me know how you go.

it may be your steering lock try and move the steering left and right whilst turning the ignition or an old car thief trick is just keep pull down to one side on the wheel until the steering lock snaps or shears and it should be free to turn after that good luck

check the vaccume module on the front axel it my have come un pluged or the electric connector hope this helps

Based on another similar problem and it was fixed driving backwards, that's exactly what I did. I drove the Rodeo backwards and then would stop and put it in gear and did this for 10 minutes until I worked the 4x4 gear loose and now all four wheels run. I must say, I created quite a sight driving backwards in a Wal-Green's parking lot for 10 minutes.