I feel for you. Your mother is unbelievable, but I do believe you. Time for confrontation. Tell your mother you will not go to the pool, if she insists on following you. You should be able to go to the get together with your friends from the pool without her. You are going to have to make this where you throw down and won't budge. If she wins this, I fear you'll never get free of her.

You're going to have to be as stubborn as she is. Tell her the two of you can do something nice together, but not the pool. If she keeps asking intrusive questions, you may have to refuse to speak to her at all. Sooner or later, you're going to have to get out of that apartment. If you wait till she is okay with it, you'll never leave.