Your children are young enough that you can just include them in eating the same healthy meals that you make for yourself. It may take a little while to make the switch for the 13-year-old, but over time they will enjoy eating healthy too. This can be better accomplished if you involve the kids in cooking and planning meals with you, and making it a fun time out of it. Kids generally love cooking, and its a challenge to them if they know they are helping mom lose weight. Added bonus is that your kids learn what is healthy too!
Exercising is a challenge while taking care of children (even though you probably already expend lots of calories chasing them around). However, a suggestion: You can use the time your oldest one is in school to exercise, and maybe you can offer to trade babysitting with another friend/s on a regular basis so that both moms get free time to themselves for a few hours. This wouldn't incur any payment since you would be trading time.
Hope yoy find some innovative ways to include the kids in your journey. Good luck. Stick with it!