I found a way to trigger the strip club events.
Get to know Erica (by visiting the gym for example) and use the "get to know her" interaction in gym once (!). Don`t interact with her any further until the strip club event chain is completed.
You need to know the sex shop owner Cara (i don`t know wether you need to interact with her further or meeting her once is enough, i usually get her slutty fast and invest as soon and much as possible)
Your aunt and cousin need to live in their own appartment. You need to blackmail your cousin / having the blackmailing option unlocked.
Your cousin needs to be slutty enough (can`t tell you the exact amount, because i usually push her sluttiness quite fast to max).
Than the event will trigger that your aunt wants you to find out what your cousin is doing at night.
You will need to see your cousin stripping at the strip club (blackmail her, search her room, wander the streets and find the strip club by chance or during the Sarah event chain, their are multiple options). After you have seen her stripping at the strip club talk to her at her room the next day and use the new interaction "i have seen you stripping" (this talk is important, just seeing her stripping and not talking to her afterwards is not enough).
You need to hire Sarah. During her event chain when you catch her stealing the breast enhancing serum (you need to have it researched) tell her to take all of them (i read somewhere that if you tell her not to take any of the serum and keep her small breasts is also okay but i never tried that, cause i like them busty). Pursue the event chain until Sarah invites you to the strip club.
If you have done all that (it`s possible to do it quite simultaneously) you should get a call/text message from your cousin that the strip club is about to close. After it has been closed you`ll be able to buy it with the help of your cousin and Cara (the sex shop owner) a couple of days later for 50k (or was it 60k...i am not sure right now ^.^, but quite cheap).
I bought the strip club in my last 3 playthroughs. It`s worth it