Radiator/transmission question

2007 Tahoe 200k plus miles.

The wife came home and couldn't make it up our snowy driveway. I noticed the back wheels spinning to get traction but front wheels weren't. I hollered to put it in 4wd and she said it was. I got in to try and noticed the data center say service 4wd. We then noticed orange coolant in the snow. I salted the drive and got it in the parking spot.The next day I'm at work and she calls to say it's shifting hard from 1st to 2nd and she's doing 30 mph and it's at 3k rpm. I told her go back home, it's in limp mode.

I get home and take it to our mechanic (just around the corner from our house) While pulling out I notice when she turns right that her front tires lock. I give all same info to my mechanic and after a few hours im told that the upper and lower lines from radiator are leaking and need replaced. I'm assuming the lines from radiator to transmission.

He doesn't know if transmission is damaged yet. Could a small leak and less than 2 miles driving damage it? Is the radiator leak why the 4wd wouldn't engage? Seems odd it all happened at once and not be related, but I'm not a car guy myself and just know basics.

Can anyone clarify for me please?
Thank you.

I doubt the transmission sustained any damage just driving a few miles limping it home. I would scan the truck for codes and start from there.

Misfires will also cause the service 4wd to display

Mechanic needs to pull trans dipstick and verify fluid level on cold indicator and it’s not a chocolate milkshake inside.

Next repair the lines, check trans fluid on warm indicator. Top off coolant level and potentially replace coolant reservoir if it’s sensor did not light up it was low.

Thank you for replies.

I think the lines were broken pulling in the driveway. There was 6-7 inches of snow and ice and my drive has deep ruts in it. When I eyeballed the reservoir it was about 2 inches below the line.

What reservoir hangs down that low?

I worded it poorly.

The antifreeze in the reservoir was about 2 inches below the fill line.

Prolly meant coolant resi. On the bright side, who ever has their trans lines break in the driveway at the end of the day, at home, with snow?

Best case scenario huh?

My mechanic just called. It's still running with rpm too high for its speed and shifting out of first hard. They recommended a transmission shop