What motivates me is knowing it's not only good for me physically, mentally it really helps with my mood and stress.
I'm also have a 2yo and an older one so know how hard it is to find the time but I make it a priority to fit it in somewhere. I look at my week and plan what I have to do and where I can fit in exercise, housework be damned :) I think the trick is to find something you enjoy. If you don't enjoy it, you'll not want to keep at it.
Do you have the 2yo with you when you do the school run? You could try a jog home once the biggest is dropped at school, 2yo in the buggy? I pay an extra couple hours daycare one day for lo so I know I definitely have one day to fit in a gym session.
Ok pool out, are there any other gyms near you? Our town has a couple of smaller ones that run classes and I prefer them to the larger, machine heavy council run one.
Do you have time/babysitter at night? Couch to 5k is brilliant to start running. 3 times a week, half hour tops, it's not much time out of your evening.
Check out online - Julian Michaels on youtube, Fitness Blender workouts, '12 minute athlete' for quick HIIT ideas.
Set small goals working your way up/down, be it weight, measurements, time or an event. Good luck!