A lot of people here way too lenient on your son, completing missing a lot of the subtext of your post. Your son is clearly disappointing, and has proven nothing but a negative impact on your business. Your mistake was assuming that your investment in your son would pay off, and gave him the expectation he would inherit things. You just need to tell him that straight, that he isn't capable of successfully running either of your current restaurants, the family can't depend on him cutting corners and ordering cheap ingredients, according to the standard you set that's egregious and disrespectful to your brand.
Your son has nobody to blame for himself for being unable to improve, adapt and benefit the business.
Your sister has proven capable and is willing to run the business, this is obviously a much better outcome for your family, and if your son went to college he shouldn't be too ignorant to not understand basic risk analysis.