I don't have children but I do work fulltime and have a busy social life. However I always make time for Exercise and healthy eating.
I schedule my exercise time. During the weekdays I wake up at 5:30am and go for my morning run. In the evenings when I get home from work (times varies but I always do it) I will do an hour to an hour and a half of cardio (this helps me vent my frustration from the day). I then have dinner. Because I live by myself on weekends I usually cook a variety of different soups and dishes and freeze them in air tight containers so when I'm too lazy to cook I'll just pop it in the microwave (quick, easy and convenient). Then I usually head out for a couple of hours. If I haven't done my evening exercise I won't head out until I do. Otherwise if I know I can't do my evening exercise I will run a couple of extra K's in the morning to make up for it.
Don't get me wrong it's a struggle to wake up some mornings and I could choose to sleep in till 7:30 am to get me to work by 8. But I tell myself that I am worthy of having a great body and after the initial struggle I feel great. Breathing in fresh crisp air invigorates me so much; it makes me glad I am out running rather than sleeping in. And some evenings I don't want to do my exercise but I force myself to do it and I'm grateful I did afterwards. I love the feeling of pushing myself just a little bit harder, sweating, knowing that I'm burning my fat away.
It's a matter of making priorities. Yes, your family and household are important. But aren't YOU? You owe it to yourself to be healthy and happy. A lot of women (with families) feel that they are being selfish for taking an hour of the day for "me" time. It's not selfishness; you owe it to yourself and your family to have a healthy, happy mum.
but i think everyones circumstances are different and you just need to work out a routine that suits you and works around your family and other things.
What Kate has written is absolutely true. Your schedule does sound busy but there is ALWAYS time to fit in exercise. Even if you can’t fit in 30 minutes to an hour a day break it up along the day doing 10 minute intervals. It does sound like you get a lot of incidental exercise in for the day. You'd be surprised at how much that helps.
treat it like you would a doctors appointment. Its not a "if I can fit it in" Its a "Must Do!"
This advice which Vanessa has provided is so valuable.
In the end it has to be something YOU want to do.