What do you do when you only have 10 minute to workout? You do what matters and you do it well. Some people like to do 10 minutes of cardio intervals, others prefer a quick vinyasa flow, while others like the trainer in the video below, love to get after it with heavy squat thrusters and the tabata protocol.
If you're not sure what type of workout would be best on days when you're short on time then just think about what you've been doing and think about how you can fill in the gaps with 10 minutes of training.
I rarely skip strength training so for me a 10 minute workout is all about yoga, core work, or cardio intervals or maybe all those combined.
Whatever workout you choose be sure to focus on form, intensity, and keep it fun. You probably have enough going on that's making you crazy so no sense in doing a workout that only adds to your busy/stressful day.
Do what works on that particular day and you'll be better off than if you skipped exercise. Check out the quick workouts section for more workout ideas or try my quick fat burning hotel gym workout.
BTW, check out those 20 lb dumbbells she's pressing. Lifting moderately heavy weights will help you burn fat and help you get skinny so be sure to use weight that is challenging.