I'm kind of relieved about that. She is not so anxious about the situation now. Another way to say it is. In a way I'm no longer so anxious about it. or I'm a little bit relieved about that. Its an expression that puts the meaning in the middle, not a lot relieved and not a small amount of relieved.
Kind of and sort of, can also be less direct ways to say something to make it softer.
Gin is an alcoholic drink and tonic is tonic water and a dash is a very small amount so it's an alcoholic drink with a tiny bit of tonic water put in it.