@RomeHome-Property-Management0 It would be foolish to trust guests who willfully violated your policy and snuck pets or extra people into the property. The only way they can meaningfully assure you that there won't be any more issues would be to leave.
But getting Airbnb's haphazard customer service involved every time a guest breaks a rule or loses your trust is not a workable solution. All they can do for you is make the whole situation ten times more complicated, through some combination of miscommunication, incompetence, and inconsistency. It's not enough to just have House Rules; you also need a plan for how you're going to enforce them.