Our favorite is what we call grill bags.
So easy and yummy.
Take aluminum foil and lay out on counter. We like to double to make it sturdy. Cut up whatever veggies you have in fridge (broccoli, cauliflower, asparagus, carrots, green beans, peas, etc). Cut up chicken (or some other meat) and put on top of veggies. I like to do the veggies on bottom so the meat does not stick. Then add some A1 and Worchestershire sauce (I can't spell it but you know what I mean).
Throw on grill and cook at least 20 minutes. DH is paranoid about meat on the grill.
We like to serve with rice. Even though your family make not like the veggies still use them because they give the meat unbelievable flavor.