Well, not really, and here's why: The longer the cardio session, the better the afterburn. "Afterburn" is technically known as post-exercise oxygen consumption, and what that fancy term refers to is your elevated metabolism after a workout. Afterburn can last anywhere from 15 minutes to 48 hours, depending on the intensity and duration of your workout — therefore, if you break up your cardio, you'll burn the same number of calories during training, but you'll minimize the number of calories lost because of afterburn.
If you really have to break up your cardio, all is not lost — but the truth is, you'd be better off finding something for the kids to do for 45 minutes while you get your treadmill on.
By all means, be sure to incorporate any exercise you enjoy. I would have an issue if you ONLY wanted to do a typical yoga routine for your exercise regimen, for two reasons: First, you need variety in your routine, and if you do the same thing repeatedly, your body will not get the best results; second, most forms of yoga do not burn as many calories as cardio or traditional resistance training. However, I do have a solution if you want to do yoga AND burn a lot of calories. My DVD, Yoga Meltdown combines hard-core yoga power poses with dynamic-training techniques to deliver a true calorie-burning workout. It’s not the yoga you might currently practice, but you can get the positive feelings you talked about while melting away the pounds.
That said all types of yoga do have all the benefits you mention and would be an excellent addition to your fitness regimen!