If you hover your mouse over the side panel bar, the cursor will change to a double-headed arrow. You can then click and drag the panel bar to change the size of the panel in either direction. This works for both the Albums/Folders panel and the Tags/Information panel.
Hmmmm . . . . I assume that you tried that and the setting is not sticky. I know of know way to change that behavior. I just tried it with some other Elements versions and it has always operated that way, apparently.
I've never seen anyone mention or complain about it before, but I can see how it might be an annoyance. I think I will report it to Adobe.
Just to add: the Keywords Tags panel retains its previous width whenever you turn it on and off using the "Keyword/Info" button and after restarting the Organizer, but the Albums and Folders panel doesn't in either of those situations.
@Greg_S. Finally got round to remembering to test this in Photoshop Elements 13, and found that it indeed does remember your custom width if you quit and restart. So it looks like this was maybe a bug which was introduced a little while ago, rather than being something that was never there in the first place 🙂