First of all --
It is going to be OK. It really is. And it is understandable that your focus is elsewheres right now. It really is. So forgive yourself for this. You aren't making excuses, just recognizing your reality, which really, really sucks at this point in time.
It is also a great thing that you are letting yourself feel crappy right now, because this is SO important. It WILL get better, and your kids are going to be just fine, and you WILL feel better, soon. I have no doubt of that.
Maybe the best thing to do right now is to take the pressure off yourself. Make the best food choices that you can, not because you want to lose weight, but because you need to be strong and healthy in order to deal with what life is handing you right now. And if you keep this in mind -- eating for strength through great food choices -- you'll find that the pounds will come off. Maybe not as fast as you would like, but you will be doing yourself some good. And your family, too. Because if you take care of yourself, you can take care of everyone else really, really well. And I know that this is what you want. And what you can and will do.
PM me any time -- I'm a fellow WW, too..