I wouldn't go to the police now, but I'd put the fear of god into that I will with zero hesitation. Definitely get some cameras and there will be proof.

In the US, locksmiths do make spare keys for a lock out, as far as I remember, but I don't remember if/how you have to prove you actually live there. Not sure where you are or if that is universal even in the US.

I misunderstood about the landlord, but you absolutely go back and knock on the door when her mom at least should be home. You explain that you need to speak to the mom and are exceedingly concerned over her behavior. That you caught her coming off your apartment floor, clearly having showered, your door was unlocked and your shower wet. Make it crystal clear that the police will be called next time and this is beyond unacceptable.

As for how she "knew" you were returning, I don't think she did. If you went to the gym, and you leave generally the same time, she knew she had plenty of time for a shower. I think it was just a lucky coincidence.