Don't know about Millie, however I was on Summit this past Feb. I believe cigars were allowed in Michaels club of course and also on the pool deck and the deck above on whatever side of the ship was designated as the smoking side. Michales club is really something, there is no smell of anything in the room, the air handlers do a terrific job.
One side of the ship is designated as smoking so you may want to find out which side that is and get a room on the other side, if you have a problem with smoke just lean over the divider as ask if they could move to the upper deck. All they can say is no.
I thought kids on cruises only brought out this much energy.
Enjoy the cruise.