We use a pet/housesitter. It does tend to run about $50 a night.

As far as the two busy working parents thing, we also have a dog walker who comes every weekday. That way the dogs get out for some fun even when the kids go straight from school to another activity. There is no way the dog could deal with that many hours in the house alone even with a dog door. On the days the kids don't have an afterschool activity, then they all play together a fair bit as soon as the kids get home. We also have two dogs so that they don't get lonely on the kids' activity days, plus a fenced yard. It is doable, but expensive. We can't imagine not having a dog, so we made it possible even with somewhat hectic lives at times.

my husband and i both travel a ton for work and play and have a small child (just one so far!) we have made it work and most definitely are glad we did! we do plan some dog-friendly vacations on purpose. for the non-dog-friendly trips, we have used a house-sitter and a high-end boarding facility. i think she gets better exercise and socializing at the boarding/daycare facility, but she's also pretty anxious there as best i can tell. in the future, we may stick with the house-sitter as it seems to have worked out great the last couple of times. not cheap. (unless you luck into a friend-of-a-friend who happens to need a place to stay for a few weeks and loves dogs. we did this once; it was perfect.)

as far as the "takes time away from the kids" thing, it hasn't been true for us so far! it was hard to give the pup proper attention when we had a newborn, but now that baby girl is (slightly) less needy and fragile, she is fascinated by the dog, loves the dog, and we're spending a lot of time trying to teach her about the dog and how (not) to treat her. baby girl is included in most of our dog activity! might be different with older kids who have their own interests, though.

i can echo the people who say to work with a rescue group. a well-socialized adult dog might be just the thing for you.