I have a 13 month old and a 27 month old I stay home with and care for - life's busy, but never too busy to exercise, but I believe you must schedule it in and MAKE it a priority, like any other chore or responsibility, or it will never get done. I just told myself that for the sake OF my girls I had to take care of myself and improve my health, so I do. I work out here, at home, with my recumbent exercise bike or exercise videos, while the girls sleep. Some mornings they wake earlier than normal, and I can't exercise because I am caring for them (I live in Alaska, so the weather is often too inclement to make going outside practical) so I wait until their nap, instead. But all I do is make a half hour of exercise a priority in my day, and almost every weekday it gets done.
Heck, sometimes the schedule is so wonky I can only move when my husband is bathing them and putting them to bed, so I do it then. But even with all my responsibilities, which will soon include homeschooling as well, there is always time for small amounts of exercise if I set my mind to it. I just tell myself it is too important to not do, and buckle down and do it. I'm committed, so I make it work
Some days are tough, definitely, but maybe look at your typical day and see where a 30 minte block of time can be carved out for movement - maybe even just marching in place during the commercial segments of your favorite show? It adds up, with just a little extra effort put in.