While there is going to be dust, you can have your contractor close off the air duct to the bathroom & seal it until he is ready to re-install it & activate it again.....also, the return duct to the air system should be covered & taped shut while any walls are being taken down.....depending on the size of your house, there may be two returns in your house, you may have to temporarily install a smaller micron filter in your other return, rather than the filters you normally use.....
Unless Epoxy is to be used, you can specify low or zero-VOC paints to be used in the remodeling, with no added costs.....you can also have your contractor give you a list of all paints, adhesives, grouts and any other types of sealants, by brand & model number/type, before any work is begun...that way you can research the list to be sure everything is safe.....
Epoxy based paints/sealants, as well as some oil based paints can take up to 30 days to lose their toxic odors.....even if the contractor has to build a vinyl shower pan for a custom shower, you shouldn't have too many worries, even the sealants used for grouting/sealing tile usually are minimal odor and usually dissipate when dry...usually the same afternoon they are applied.....
People in different parts of the country think of mud rooms differently, but if your mud room is going to be a wet-sink utility/laundry room, you shouldn't have any further concerns than what I've already mentioned.....
Good luck.....
hope not! This is happening on the main floor of my house, and my keet is in my room on the second room, if it helps 
LOL
