Years ago, I was a partner in a brake shop here in central america.
Given the information that you gave in your listing a couple of things could have happened.
1) The pistons on your rear calipers got stuck and caused consistant braking. This could be due to the seals within the calipers gone bad.
2) What I really suspect is that the seals in your master brake cylinder went bad and caused consistant braking on your rear tires. That is why both of them were hot. If it were just one tire I would suspect that it was just the caliper.
You did not mention what vehicle this is? I do not know if there are additional valves or hoses in the braking system or it could have been caused by the ABS? Though I highly doubt the ABS.
Your line of attack:
1) Repair rear calipers. (new pistons and seals)
2) After this, check your master brake cylinder. if bad change out the master brake cylinder also.
3) If there are additional valves or hoses check these also for blockage.
Insanity: doing the same thing over and over again and expecting different results.
2006 - Suzuki Gran Vitara (2.0 L fully equipped) Like this car so far except for trying to put on the seatbelt.
1988 - 190e - 2.3L - 172K miles (It now belongs to the exwife)
1999 - Chevy Blazer LS Fully Equiped - killed it June 2006
2001 - Honda Civic EX - 68K miles (sold June 2004)
1963 - 220S - Dual Carb 6 cyl. (sold)
1994 - Yamaha WaveRaider (fun to ride)