Welcome! I would highly suggest ignoring the scale for a while if it causes you trouble. Pay attention to how your clothes fit and/or take measurements. That will show you your progress much better.
If you enjoy the high from a hard workout, try PBF and sprinting. I get the same post-exercise high from those as when I used to do long exercise classes. But I'm done in 20-30 minutes and often sore the next day. That will leave you with extra time for your twins! If you enjoy the alone time, then go for a long walk with some great music. Your body will get more out of short training and long walks.