Your landlord isn’t allowed to keep a key to the apartment without your consent. If you want to be honest about the situation, neither landlord nor caretaker can gain access to your apartment, then the only solution after moving in is to change the locking to the house.
As a tenant, you can do this, but you can assume all of the costs for yourself. There are no Clauses in the rental agreement that prohibit you from doing that. This applies to the security of a secure home.
This is important: You must maintain the lock the landlord provided for you and return it when you occupy your house.