Kymopoleia understood the consequences of these actions and she was ready to accept them. Anything to change things.
It was easy enough to find out where Poseidon was going - in his arrogance he feared nothing - and it was easy enough to get what she needed once she was there. Now she trekked through the park, following the feeling of her father. He'd know she was coming by now, but what was he going to think of it?