Separation anxiety is very common in young children who leave their comfort zone. Maybe it is changing activities that pulls the trigger.

I think you're doing a great job with her. It's important that you can feel/acknowledge her pain and it's smart that you have a "crying spot" so you have some control. I wouldn't try to reason with her though because it's giving her the power. I would give it a few more weeks and if it doesn't get better, I'd probably term her for both your sanity and hers.