Need help with parents 02 explorer(rear axle?)

[hfdff]

So here is the problem. While putting it in reverse and letting off the brake the left rear tire will most of the time shutter (as I can best describe it). if I hit the gas it will make it worse. Sometimes when I hit the brakes it will make sound that something has seized up, it is rather loud at times. It will only do it in reverse, going forward it does not do it. According to them this has been going on for about 2-3 weeks.
So here is what I have done, when I went to go look at it I noticed that left rear tire had a lot of play in it so I changed the left rear hub. that was last week( it was trashed)
-while I had up on jacks I did notice that axle seals had been leaking for how long I'm not sure, but it looks like it has been awhile.
-When I drive it I do notice a humming sound as I have heard people describe on here and go away when I let off the gas.
-When I turn the tires I notice as I would say is a lot of play when turning it back and forth.
- At the drive shaft I noticed some up and down play where it is connected to the rear axle.
-Up on jacks I put in reverse to see if it would still do it the left wheel doesnt turn but I can see that it wants to shutter.
-I have taken the drain plug out and drained the oil to see if I can see anything obvious, I did notice that the some of the gears do have wear and while moving the tires back and forth that there is some obvious play at the gears.
I know very little about rear axles, all I know is that the have gears that make the wheels turn and you can run into some real problems with them if not taken care of. If the rear axle is bad would it be better to have it rebuilt or roll the dice and get a used one from a pick a part. my parents are on somewhat of a fixed budget. Almost forgot the rear axle is a 45.
Thanks for the help.

 

[donalds]

I'd go for the junk yard route install new seals new oil

 

[hfdff]

I decided to remove the rear axle. Here are some pictures of how the gears look. Is this normal wear or is it excessive? The top and bottom gears have play in them not just up and dowm also the ones on the side where the CV axles connect to. The gear in the last pic also has some play. When I rotate the flange where the drive shaft connects sounds like a click clunk sound. Ill post a video of it if i can.

 

[hfdff]

I forgot to ask would the ABS sensor on the rear cause the left rear tire to shutter like that?

 

[MrPulldown]

I forgot to ask would the ABS sensor on the rear cause the left rear tire to shutter like that?

yes. Usually when the hub/wheel bearings go bad, there is too much play and the ABS sensors throw a code and don't work right. The new hub should come with new abs sensors.
The herky jerky back up is the abs sensor and thinking there is some slip and throwing the truck in and out of 4wd.

Gear teeth do look a little worn but fine.

hmming is normal.

 

[hfdff]

yes. Usually when the hub/wheel bearings go bad, there is too much play and the ABS sensors throw a code and don't work right. The new hub should come with new abs sensors.
The herky jerky back up is the abs sensor and thinking there is some slip and throwing the truck in and out of 4wd.

Gear teeth do look a little worn but fine.

hmming is normal.

The explorer is 2wd and it doesn't have any abs codes and the shuttering only does it in reverse. Would the rear abs sensor cause that?

 

[MrPulldown]

The explorer is 2wd and it doesn't have any abs codes and the shuttering only does it in reverse. Would the rear abs sensor cause that?

Mine only did it in reverse while turning. Any bad ABS senor could have done it. But I threw an ABS light.