I'm honestly surprised that nobody sees this from the OP's POV. First, she DOES let her kids have sweets. They get a cookie in their lunch every day, and there are desserts; I'd LOVE it if someone was making cookies, pies, etc., in my house! What's the big deal if she doesn't feed them candy? I can't remember ever buying candy for DD just "to have" and she never snuck anything from the baking supplies (although I rarely bake, so my supplies weren't very tempting). Kids don't die from not having chips in the house. We rarely have chips... high salt, high fat, high calorie filler-food isn't something I choose to spend money on. Oh, we have chips sometimes- I probably buy 2 bags a year- and DD could always have whatever she chose to eat when away from home. It doesn't sound to me like OP forbids sweets, chips, candy, etc.; it just isn't stuff she chooses to have in her home. Besides, these are BAKING supplies. It's not like there's candy laying around and she's saying "look what we have that you can't have;" these are baking ingredients, stored away on the baking shelf, in the back, out of sight.
I didn't read her post as an issue with candy. It seems to me that she is concerned that her son (as opposed to her other child, her DAUGHTER) feels no compulsion about taking things if he wants them, even things that he knows he's not supposed to be into, and that his mom would say "no" to if he asked. Regardless of what instigated the situation, I, too, would be very concerned if I learned that my child would choose to do what he wants to do even when he knows he is not supposed to. How do you instill honesty and responsibility if a child chooses to do whatever it is he wants to do, regardless of what he knows is right or wrong?
I don't have a lot of suggestions here, OP. DD has always known that, while there are things she isn't allowed to do and would be in "trouble" for, it's nothing like the trouble she'd be in for lying to me, or sneaking. I have always been very clear with her that we need to be able to TRUST her. As punishment for sneaking the candy, I guess maybe, since your son cannot be trusted to stay out of the baking candy, I'd get rid of it and make sure the family knows that there won't be choc chip brownies, m&m cookies, pb blossoms, etc., because you can't trust the kids not to eat the candy. (I'd actually make the regular sweets but not put choc chips or other candy in the cookies, bars, etc.) Seems a reasonable response... I can't trust you with it so we cannot have it. However, not knowing your DS and what motivates him, I have no suggestions for figuring out how to teach your son to make the right, trustworthy, responsible choices instead of doing things because he wants to.
And FWIW, don't feel like you are the only one who limits what she offers her kids at home. We never have, on a regular basis, cookies, candy, soda, chips, pudding/dessert cups, brownies, cakes, pies, filled cracker/cookie sandwich packs, etc. in our house. Our big weakness is ice cream, which I try to purchase only once a month, in a 1/2 gallon container. heck, if it were here, we'd EAT it... just what we don't need!