Can They Do That II? Michigan Legislators

Can Michigan legislators force one of their colleagues to shut up?  I posed that question yesterday to my friend Ignoto, the distinguished constitutionalist, and even as my finger tripped over the keyboard, I suspected I knew the answer: who's going to stop them?  Legislators (cf. the Wilkes episode) fought hard to secure their immunity from higher authority; they aren't like to yield it to anyone, no matter how badly they abuse it themselves.    And in some sense, they've got to have the power to control member behavior.  What if legislators start beating each other up in the chamber (there's a fascinating Wiki)?

Ignoto responds this morning with an email suggesting I am on the right track. I did not know about the Congressional jail.  But here's Ignoto, on "can they do that?"

It's a hard question.  At the federal level, the Constitution gives each house the power to discipline members, including imprisoning them (there used to be a jail in the Capitol for this purpose).  They could probably punish a member for telling another to f--- off on the floor of the house.  I suspect most courts would view this as a political question and wouldn't touch it. I'm not aware of any decisions on point.   I don't think you could limit a member's right to vote, but speaking is arguably different; I not sure what the full dimensions of a right to speak would be, given that debate is regularly limited in all kinds of ways and you generally can't speak without recognition from the chair.
No doubt a stupid use of this power, but it may be permissible.

 All sounds believable to me. 

Afterthought: just on a lark, I went back and checked an online version of the infamous Starr Report into the misbehavior of President Clinton.  Sure enough, the offending Latinism appears there twice.  Oddly enough, the word "cigar" appears 19 times.