I dug thru records (actually receipts) this AM and found where the rear hose was replaced in 2007 as part of a brake job. As you can see in the photo - the rubber hose looks pretty healthy.
Doesn't matter what it looks like on the outside, brand new hoses have swelled up on the inside and caused the brakes to stay on. Symptoms are usually exactly what you've described, the brakes work fine initially then start to drag as the drive goes on. Sometimes to the point of locking up solid until a bleeder is cracked to relieve the pressure. Most don't lock up that tight, they usually bleed back once enough pressure builds up. But in the meantime your brakes are dragging.
2007 was 13 years ago too, that's not new. I would expect more from stainless lines, but plain old over-the-counter rubber lines are a quality crapshoot nowadays. And have been since before 2007.
It could be an issue with the return springs too, but you can't rule out that hose just because it "looks healthy".
As I look again at the left rear wheel - it appears that the bottom edge of the front shoe is separating from the lining. Perhaps no surprise since that wheel was smoking hot yesterday. Unfortunate since its was installed about a 100 miles ago.
I have seen some pretty burned up brakes,what you have there is some inferior brake shoes.If i was in this situation, i would be seeing about warranty.
Either way, those shoes are toast. I'd be surprised if anybody warrantied a scorched set of shoes, but even if they did I dunno that I'd want the same brand shoes if they separated so easily.