I have this mustang for past 6 months and had nothing but problems.

The car was severely shake after 35mph, Took it to 2 different garage and they said the differential need replacing

I have never heard of rear differential going bad at 110000 miles.

Need help to figure out the best way to get this fixed.

 

well wouldnt hurt to jack it up and take a look at your rear diff, but it could also be unbalanced wheels, when was the last time you had them balanced?

 

Rotate your tires front to back to see if the shake follows from the rear to the front. If it does, it's a tier issue, if not, it a rear suspension/drivetrain issue....assuming the shake is coming from the rear right now? Feel it in your **** or hands?