I would invest in or make some scatter guards like mentioned, they don't seem to eliminate the poop and hay from being thrown everywhere but it can cut the amount down. The cheapest way is to just weave fleece between the cage bars near the bottom, but wood or metal last longer and are easier, but do cost more.
I also keep a broom by the cage so I can sweep up around the cage. Depending on the cage you have, if you are really busy and just want to make it look nice quickly you can even just sweep the hay and poop under the cage and then sweep it up later when you have time, at least that way you aren't walking through it and spreading it around the room. I also use a shop vac instead of a regular vacuum, no worry about it getting clogged or the hay and sticks being hard on it and burning out a motor.
For the dust bath I just take him to another room for it, rather then putting the dust bath in the cage for bath time. Once he is done I take him back to the cage, and less dust ends up all over the cage and in the room. Also I use a gallon jar for the bath so the dust is a bit more contained. For the most part the fur should be shed out during the baths, but if your chins need a little help you can try brushing or combing them before the dust bath to help loosen the fur and get some of it out before the bath. A soft bristle brush works well if the fur isn't matted and just shedding, and some chins really seem to enjoy it.