The guy who wrote the instructions didn't have two babies to contend with but five attorneys who are covering their liability.
I have done a number of houses in the last thirty years and rarely has anyone had to move out of the house. You may have to do one room at a time. If access to bedrooms or other rooms is a problem you can leave a two foot "sidewalk" to walk on following the cracks in the boards.
Personally I would use an oil based Polyurethane and get lots of air movement to speed up the drying time.
As far as moving back in on finished floors I would't worry so much about that because you are looking for sealing the floor to make it easier to maintain.
I would suggest maybe planning a day trip and leave just after coating the floor so the little ones aren't exposed to the fumes.