Hi hal
My guess would be by what you say, is that the hunger your wife is feeling, is related to her high BG's, when the BG is high the body can't use the glucose probably for energy, so signals for food to create energy, bit of a visious circle at times, eat the food BG increases, and the hunger increases etc
I'm assuming by your wife list of medication that she's a T2 diabetic, byetta and insulin aren't generally prescribed together, and she is on one hell of a congotion indeed..
Does your wife actually carb count, as this would be probably a good idea if she doesn't.. As one way of helping to control the levels is knowing the amount of carbs per meal/snack you are eating, also what types as different types will asorb at different rates, carbs such as found in pasta can take quite a while to asorb and impact on the blood glucose..
I would suggest that you note down of all the foods she eats, types and amounts so that you can hopefully find out the foods or amounts which are causing the problems and high readings, and take regualr BG readings, fasting, before and after meals (and snacks if necessary) and at bed time, so that you can compare foods/amounts/types to how her blood glucose has reacted..