What surprises me is why civilian Michael agreed to be driven by the bodyguards to Kay's hotel
Sure, he could have said, "No, Sonny, I'm going on my own." But that would have set up a confrontation with Sonny at a time of great stress. Better to go along with it, don't make an unnecessary scene.
Notice a shift of values: Clemenza is so confident of Mafia's "code of behavior" that he says Michael doesn't need an armed escort to the city because "Solozzo knows he's a civilian." But, by the end of the movie (~10 years later), civilians drop like flies: the hooker with Tattaglia; the bodyguards and chauffeur with Barzini, everyone in the elevator with Stracci. For that matter, Roth didn't care if his killers whacked Kay and the kids if they happened to be in Michael's bedroom in II.