How big is the family, and how big are the dogs? If your space needs aren't overly-substantial, look at the Ford Escape. It is exceptionally quiet, a very comfortable ride, and has plenty of power when you choose either EcoBoost engine. The 2014 model has all of the new-model bugs sorted out. We've taken a family vacation roadtrip with two adults and three children, with some minor off-road travel as well.
The in-cabin tech on more-optioned trims is great for families with pre-teens and teens, as there are USB ports and even 110V power available to keep their i-devices charged, among other handy features. This model has a number of redundant controls for climate and stereo, so there's no menu-hunting needed with a touch screen just to adjust the temperature or change the station. Voice-activated features are especially helpful if you're in one of the many and ever-growing list of states banning the use of mobile devices while moving.
If you need the space of a true full-size SUV for your dogs, this might not be for you. It fits our family of five, which includes two teenagers. (I'll refrain from suggesting any full-size models, as I don't have enough hands-on experience with them).