My dog won’t stop stealing food when we’re not looking

We have a puppy-mill rescue Bernese Mountain dog (age 3 now, we've had her since five months old) that has figured out how to access any food left unattended on any table or counter level surface for even a minute. She's been on moderate food restrictions for several weeks because she is overweight per the vet – we're following their guidance.

We have five kids, mostly young, so it is simply not possible for us to prevent any food from being unattended. This week, she probably got close to $100 worth of food, mostly treats that we had bought (and then rebought and then god damn it re-re-bought as replacements) that were intended for one of our kid's birthdays today. One case happened when we got interrupted in the middle of putting groceries away. This morning, I had left the cupcakes I bought for her to take to school on the counter briefly (I tried to put them where I thought the dog couldn't reach) while we went upstairs to brush teeth, but they were gone when we came back downstairs. I'm about to lose my mind, especially because she also chewed up multiple library books overnight (she seeks them out from couches and side tables where the kids leave them), which seem tastier than regular books for whatever reason. She's probably cost us about $500 in library books in the past couple of years. (Don't even get me started on what she's done to the new carpeting, even though we have a dog door.) We cannot afford this, especially right now.

We took her to obedience training in her first year (and she wasn't our first dog, so we had some know-how already), but I really don't know how to use those skills to address these sorts of behaviors that she does when our back is turned, especially because the rewards of eating a whole package of cupcakes are so large.

Does anyone have advice? We can try to do better with keeping all food out of her reach, but I'm afraid that's nearly impossible for a house like ours. I'm starting to wonder this dog is a poor match for our family.