I think people are thinking too much in the extreme. Most dogs would probably be suited with a bit of commone sense and crate training.
Eg perfect day and a dog proofed outdors area, let him/her run free when there is no-one home.
Forecasted storms or extreme heat, crate for the few hours you/your kids are not home, then let them decide when you are.
Excercise doesn't just mean walking or specific dog related stuff.
My kids get home and go straight to the backyard to kick the ball around, and our Boxer pup does the same. (OP said the family has kids)
Being that he is crated during the day, when we're all home, all he wants to do is go outside and roam around the backyard. Only saying this as Boxers are extremely people orientated, yet believe it or not, he enjoys time exploring outside.
The OP said it would be a mix of indoor and outdoor, and in my view, with commone sense, and crate training (including sleep indoors in crate) then pretty much most dogs will suit.
My biased view - get a Boxer :)