If you do strength training at home, as I do with two kids too, you don't need much preparation. I just take off my t-shirt, do some pull ups, push ups, squats, etc. following a well thought plan, and most of the time the shower is not needed. You don't even need to do all the exercises in the same time slot. You can do pushups as you watch your baby, a few pull ups while your watch your son wash his teeth, etc. Not changing, not much preparation.
I apply this method and it is amazing how stronger and leaner I am now. And doing pushups, some cardio is also done.
I do cardio while bicycling to the office (no clothes changes needed again; maybe just the t-shirt in summer), and walk up the office and home stairs (4 floors in both cases) two steps at a time.