The way that immunity is taken away is that Congress expels them. See Article 1, Section 5, Clause 2. It's all in there.
See how brief it is ~ Congress, by design, is authorized to protect itself and may even call out the militia (presumably to repel an invader, or dispose of a tyrant).
As do you. As do I. Congress makes the laws. That's what it's there for.
The way that immunity is taken away is that Congress expels them.
I don't know where you're getting this idea that members of Congress have some sort of super-duper legal immunity until and unless they're kicked out of Congress. Patrick Kennedy, to name just one, is still in the House, and is still under court supervision for DUI. He was arrested and struck a plea deal. There was no magical congressional immunity to make it go away.