Before Arkham Origins Incident
Before the events on Christmas Eve, Jervis Tetch presumably used his shop to commit his crimes, while also selling hats.
Arkham Origins IncidentDuring the events of Batman: Arkham Origins, Mad Hatter used his own hat shop as his secret lair. Here, he held a young woman captive, believing her to be 'Alice'. Batman, however, infiltrated the shop and managed to stop Tetch from murdering the woman. Mad Hatter was apprehended by the GCPD and sent to Blackgate Prison.
Cold, Cold Heart Incident
Between Arkham Origins and Arkham City Incident
The shop was presumably closed down after Tetch's arrest and had not been used since.
Arkham City IncidentOnce incarcerated into Arkham City, the Mad Hatter failed to reclaim his hat shop as his secret hideout. He went on to find an old stripper club and claimed it as his. Batman, taking what he believed to be the cure to the Titan Disease, passed out and woke up in Tetch's Lair, where the latter used his brainwashed henchmen to attack Batman and make the Dark Knight work for him. Batman, however, managed to defeat all henchmen, before knocking out the Mad Hatter himself. Batman left him to sob over his destroyed hat, and he remained inside his lair for the rest of the game.
After Arkham City Incident
Arkham Knight Incident
In the Arkham Knight's Militia HQ, an abandoned shop can be seen with mannequin's faces that are replaced with rabbit masks and suggesting that this was Tetch's old hideout.