My pup is about 8months now and is a complete TERROR when he is not exercised. I to am a very busy person, I do not have kids but I work full time and am doing my Masters so I can appreciate how busy and stressed you are, it is not easy to juggle so many things. I do anything I can that will keep his mind active, his body moving and his mouth busy! For example, in the mornings Gunner and I are up before the sun and we go for a 30 minute power walk (I power walk he saunters and pees on everything), thenwhen we get home I give him his breakfast, which is a big frozen raw meaty bison bone, that occupies him and helps to tire him out more while I am getting ready for work, then I crate him up and give him a giant antler.
When I am home, I take every spare moment and we play in the backyard or in the house, this play will be either mental or physical or a combination, this can range anywhere from 20 mins to over an hour depending on my schedule. When I put him in his crate I try to always have something to occupy him, somthing that is safe for him to do that does need need supervision, like his kong with a treat in it.
I find that even in my busiest times if I can only squeeze in 15-20 minutes of play in the morning, and then at least 30 mins in the late afternoon, and about 20-30 minutes in the evening before bed, he is a completely different dog (for the good) than if I were to only let him out in the yard to do his business. Excercise, albeit mental or physical y (both or important) a few times a day makes a world of difference!!! It helps with his separation anxiety, his destructive behvaiour in and outside of the house, and his obedience, and is fair to him, boredom can lead to many many behaviour problems! A tired dog generally speakign does not feel the need nor have the energy to eat my coffee table! A bored dog however, does have the energy and the will to rip up my cedar bushes and dig to China in my backyard!