It’s not so strange that only one battery would get hot. It’s a lot harder to short the terminals of an AA battery than it is to short the terminals of a 9v. The one that got hot was probably “just right” in the foil and/or coins so that it shorted and maintained contact. The other one either didn’t short at all; or if it did, the terminals did not maintain contact with the metal.
I think you’ll find the battery has cooled down by now, but it took energy to generate the heat. It’s at least partially discharged.
There’s nothing wrong with putting a battery in a handbag. Just make sure there is no metal for it to come into contact with. I suppose if you want to be sure it’s isolated you can put it into an appropriately-sized plastic pill bottle. Or you can keep a couple of batteries in a plastic cigar tube. Or put electrician’s tape over the terminals.