Just holding it in shouldn't stress her out, just make sure to be gentle.
Is she shaking because she's cold? When you give her a bath just try to get her vent area wet, that's the only place that needs bathing.
It is a prolapse.
Keep doing the treatment your doing.
Try and hold the tissue in for a couple minutes, try that a couple of times and see if it helps. I've seem worse cases of prolapse here on BYC, hers isn't too bad.
Here's an article.->...