In order to avoid the time involved in checking into London lodgings twice, I'd highly recommend going straight to Bath or Salisbury (for Stonehenge) on the day you fly into London. You will be tired that day and may not be in much condition to sightsee, so you may as well do something productive with your time. This way, you don't have to rush back to London on the last full day of your trip; you'll already be there, enjoying yourselves.
Are you planning to use public transportation to get around? That would work fine for the places you've mentioned. I would definitely not recommend renting a car and driving to Bath on the day you arrive.
I don't have kids, so I can't comment on what yours might enjoy; I have no interest in Stonehenge myself. Others can give you ideas suitable for kids, but they'll need to know how old yours will be at the time of the trip.