I don't think there's any secret to getting motivated, you kind of just have to fake it till you make it, you know? For the first few weeks/months you'll be uncomfortable, you'll be stiff and sore, you'll hate it. But if you want to lose weight and feel confident in your body again, these are sacrifices you have to be willing to make.
If you're looking for specific, actionable advice here's what works for me:
For starters, do your absolute best to limit empty calories from things like junk food and sugary drinks (think soda, juice, and sweetened teas/coffees). To really lose weight you need to create a calorie deficit (usually about 1500 daily is enough to do so) and I highly recommend looking into an app like www.myfitnesspal.com/ to count your calories. If you're honest with yourself, you'll quickly see how much of your daily allotment is getting eaten up by junk.
The next change you want to try and make it to make sure you're actually drinking enough water. Our bodies need about a gallon per day to operate at peak efficiency and the average person falls short of that number quite a bit. This is another area where having an app on your phone to remind you and help you keep track can make a world of difference. I use a generic app called "Water Tracker" that I found on the app store.
As for exercise, I'm not sure of the specifics of your situation, but I can imagine that with three young kiddos that going to the gym on a regular basis is going to be nearly impossible, so working out at home is probably going to be the path forward for you. I'm a big fan of Beachbody and their at home workouts, so I'd definitely recommend starting there. They have free trials available for most of their more popular programs so if anything I'd check a few out and see if they appeal to you: www.beachbody.com/product/fitness_programs/online-workouts-videos.do