You're smart to think about the challenge of feeding your kids too, because it has been a bit tricky to feed our daughter while on the plan. She'll eat the protein and some of the veggies and then I've just added a starch for her meal - pasta, garlic bread - rice - something I can make easily and just for her so I'm not tempted to eat it. If she doesn't like the veggie I'm making for us, I substitute fruit for her, figuring she needs that too.
One good thing is that she's in the habit now of taking a multi-vitamin because we always take them with our evening meal so she takes one right along with us.