This is not a post about trying to work out with no rest because your kid kept you up all night although now that I am saying that maybe I will do one in the future. I integrate strength training into my exercise routine a couple times a week. This is where I work on upper body and core strength as opposed to working on cardio. It is common when lifting weights to lift then take a break and wait for your next set. Instead of resting during the break I switch and work a different muscle group. Most often I switch between upper body and core but I do integrate some legs into it as well.
People have different goals with their exercise so tailoring your routine to your specific goals is important. Whatever the goal is it is very important to work out the whole body if for no other reason to avoid injury. I have a dumbbell routine that I have been doing for years that integrates high reps with the dumbbells while doing different core workouts in between each set. This method of exercise allows me to keep my heart rate up for the entire workout.
I began this routine long before I had kids and did it by design to keep in constant motion. The benefit I have realized since having kids is it allows me to target more muscle groups in a shorter period of time. I give myself an hour for the work out and 45 minutes, give or take, is constant moving from rep to rep and work out to workout. I then give myself 15 minutes for cool down and stretching. Block out a set of time, design a workout that targets your goals, and jam as much into that period of time as you can.