sanding and refinishing hardwood floors in entire house

My house was built sometime in the 50's, and then later wall to wall
carpet was added on top of the hardwood floors. Now that my three kids
have sufficiently ruined the carpet, I plan to pull up all the carpet
and refinish the hardwood. Will there be any significant problems with
doing the different rooms at different times? Otherwise I have to
concern myself with moving all of the furniture out of the house at one
time. My personal feeling is that if I do that, then I might as well
move it into a new house.

You might consider renting one or more storage lockers for your
belongings and just move completetly out while sanding. Sanding is a
gruesome task and yu don't want to do more than once. Put your family
in a nice hotel and they wont' mind.

My preference would be to have a storage unit dropped off.
Move out for a week. Have the floors done by a pro.
Would give you a chance to paint at the same time. Thoroughly clean &
then move back in.
Major PITA yes, but it could all be done in a week.

One or two rooms at a time with sanding & dry times for the floors,
moving back & forth, & you'll be sick of it before it's over. It will
take longer than you think this way.