Oh sweetie, don't be so hard on yourself! How about when the kids are out you go out and buy some lean steak and/or chicken and roast them and cut them into bite sized portions for the freezer? That way of you're out and tempted (or even at home) you can defrost a cube sized piece of meat to satisfy the urge to chew? Don't give up and stop kicking your own butt .... You're doing amazingly well, but you're human. Things happen but you've got to stop sabotaging yourself. You deserve success and can achieve it, and your girls need you happy, healthy, and active (sounds like your ex is a twat too - then again, they are exes for a reason!).
Write off yesterday, man up, and keep going - I know that feeling of resisting one thing only to get home and stuff my face with an unsatisfactory substitute. Change your mindset: this isn't deprivation - this diet is reward. Yes, I said it and I'm not crazy
Every minute, every hour, every four hours is a triumph. Every pound off is a blessing to your internal organs. Every day you fight against 'helping' the kids out with their tea you are negating the negative feelings and subconscious pain from life's hardships and disappointments. You're saying: I'm worth good things, I deserve to be the sexiest, healthiest ME I can achieve.
You're a wonderful woman love, don't give up just yet, you have more success ahead of you xxx
Ps: Run (don't walk) to watch some inspirational Dual Dynamics videos!