Have been hearing a rattle. It sounds like it is

Rust and bushing wear are problems with the rear suspension components in these vehicles. You did not mention the year, but you probably have leaf springs back there. You need to check the shackle bolts and the leaf retaining rivets for loose or missing parts. If you have coil springs, check the lower spring bumpers - one or both my be badly worn or gone. And yes, any bushings may need replacing.
As far as the brakes are concerned, that is probably the noise you hear. You need to have the shoes replaced right away, and since they are that badly worn, the drums will need to be turned or probably replaced.

Check all the bushings and make sure they are not loose. General Motors bushings are prone to cracking.

take the wheel out and make cure the Bering wheel is good

I had a similar problem with my 2006 Montana. It ended up being the foam shield donut looking thing that stops the parking brake cable from hitting against the middle of the rear axle. Fixed it with foam plumbing insulation and electrical tape. Better than new. Hope this helps.

if the rattle is always there when the car is started then you might have a loose/damaged exhaust hanger. i have also seen an instance where it was a loose heat shield. if the car is RWD and you only hear the rattle when the car is rolling then you might have a shot set of bearings on the U-joint connecting the driveshaft to the differential, this is a major safety hazard and if you think this might be the case, you should have the u-joint examined by a licensed mechanic IMMEDIATELY.

If it's making a clunk noise when hitting bumps, check the mounting plates and bushings that hold the rear end to the frame. GM made these plates out of aluminum and the bolts that go through the plate and the bushings rot out and the rear end slams against the frame.

hard to help with out hearing for my self, try getting different opinions from 2 other shop. may be worth it. 1 to be a transmission shop if it is a trans problem.

It's probably the rear sway bar links. If you can jack your car up and check right behind both rear wheels you will be abale to see the sway bar which is connected to short links about 5in long with ball joints.

If either of them are broken or not connected anymore it can cause some pretty loud noises when you ride on rough roads or hit bumps. They run about $35 per link so it's not a very expensive repair.

hi the rattle from rear shocks may well be the lower anchor bushes that have dried up and cracked or shrunk on the fitting thus allowing the lower mount bolt to rattle about on its pin? if your shocks have covered high milage or show sign of leaking? then it would be beneficial to change them? but you can obtain the bushes and are easy diy if you wish ?