I know this is an old thread, but imma jump in here with some real, workable advice for a big family on a budget.
Just concentrate on going high protein/low processed foods. When I first started out I was eating the hell out of those grocery store roasted chickens. Get the best hamburger you can afford and make cheeseburgers without buns. Get frozen veggies, no matter what kind - peas & carrots, whatever this kids like, steam them with butter and serve that. If you try and do grass fed beef on a budget - I mean, it's $9 a pound here in San Diego! There is no way. There is a brand of organic sausages - Aidelle's. It's in Ralphs, Von's etc - chicken & apple is AMAZING cut up in scrambled eggs. They also make little ones, like those little smokeys, that I take along in a baggie for snacking - chicken & pineapple is great too.
Look - starting out is HARD. Changes are hard. Go easy on yourself. Concentrate on shopping on the outside isles of the grocery store, stay out of the middle. Leave out bread and tortillas entirely. Make taco night - make it with packaged taco seasoning, just serve it in a bowl with cheese, maybe salsa, buy good avocado to go on top. DO WHAT YOU CAN.
Get your kids used to water or orange juice instead of soda, for instance. Slowly cut out dairy. Start buying full fat yogurt. Steps, it's all steps.
I totally understand the budget vs. the TOTAL PRIMAL ZOMG ONLY ORGANIC GAH! It's frustrating. If you need more ideas, let me know.
I could see that, if not actually disgruntled, he was far from being gruntled. ~P. G. Wodehouse