Skits - we actually gave up on threading the meat and veg on the skewers. Could never get it all done at the same time. Now, we thread just the meat on the skewer and cook the veg in a wire basket on the grill. Generally use squash/zucchini, mushrooms, cherry tomatoes and red onion, all basted with a little reserved marinade. Easier to stage the veg cooking if needed. We like a marinade of lemon juice, olive oil, garlic and oregano.
The yellow squash I used had a very hard outer skin. Not sure what I did wrong with growing that one. Heat? Not enough water? Left too long on the plant?