Absolutely backwards. Long rests should more restricted, at the very least they should require the party already be in an outdoor area isn't within the bounds of a town or city. Also both should advance time properly so that time critical quests are affected.
Make it two short rests per Core Rules
As per core rules would be unrestricted. The restriction is on your healing during short rests, not on short rests themselves. This is the entire reason that warlocks are even viable as anything more than a dip class in PnP as short rests are limited only by the DM's willingness to let you have them uninterrupted ie. "if you take a short rest somewhere dumb, something bad might happen AND you wont get your rest so.... don't take the piss"