In this society, superstitions regarding right- and left-handed people are accepted as fact. (I'm going to be politically incorrect and call them "righties" and "lefties" henceforth). To overly simplify things, righties are considered stronger in science and math, so they are in the highest caste and serve as leaders, scholars, and professionals. Lefties are believed to excel in the arts, so they are part of a lower caste consisting of performers and craftspeople. The third and lowest caste is composed of the physically and intellectually disabled, who are domestic servants and menial workers (and are forbidden to breed).
There are specific laws regarding lefties. They are required to expose their left hands at all times, so everyone can see their status (usually this is done by rolling up or cutting the sleeve). Because they are considered "incapable" of academic learning, they are not allowed to study math and science, and are banned from righty schools and universities. They're also banned from many public buildings used for recreation, like libraries, theaters, pubs, etc. They are allowed to charge a fee for their services, but 9/10ths of their earnings go to the treasury, so they often live in poverty.
As long as they obey the rules of their caste, lefties are free to live their own lives. They have formed a kind of guild system in which they associate with others of their trade. Each guild has its own specifications for joining; members must show a certain level of skill or commit to a certain quota. Some restrict their membership to kin, but many are willing to take on apprentices. In general, lefty children born to lefty parents will train alongside their parents and eventually join their family's guild, but there could be exceptions. A lefty who shows particular talent/promise in an art might be apprenticed out to perfect it.
There is limited social mobility. Although people born as lefties can never join a right-handed caste, no matter how talented, a lefty who is particularly in demand might gain a certain social status. They are respected among their caste, earn impressive wages, and live influential lives. A lefty born into a right-handed family also has certain privileges. They are considered part of the lower caste, but their parents might use their influence to secure their futures. (My story is about a physically disabled boy born to a powerful politician, and his father uses his pull to get him into a silversmith guild even though he is incapable.)
So here is my question: what would happen to a right-handed child born to two lefty parents? This child has received little to no education and knows nothing other than their family's trade. It's hardly likely that righties would willingly adopt these children. However, the probability of a righty being born to lefty parents is extremely high: about 75%! While the probability of a lefty being born to righty parents is about 1 in 10, which my story can support. (See this link for statistics). What's more, it would be common for lefty parents to force their lefty kids to use their right hands if it allowed them to join a higher caste.
Now, I could easily say that once someone is born to lefty parents, they are of a lower caste no matter their handedness. But I'm wondering if there's some scientifically plausible way for the higher caste to ensure that at least most children born to lefties are left-handed. Over a long time period, inbreeding would be an option, but my story doesn't allow for that (the lefties in the story are 2nd-3rd generation at most). I'd be willing to consider unethical solutions, but keep in mind that this society is not advanced enough for genetic engineering to be an option.
Is there another way for righties to make sure that left-handed parents give birth to lefties? If not, what system can righties institute to reduce the chance of righties being born to left-handed slaves?
In case this is relevant: the society is a religious one. They believe people are born left-handed (or disabled) as a result of the sins of their parents (usually related to impure thoughts), and that they must serve as "atonement" for their ancestors' actions. Righty parents who have a lefty child generally consider this a mark of shame, so they willingly condemn their children to a lifetime of service. If it's possible to reduce the number of righties born to lefty slaves, then in the rare case such a child is born, their sins could be considered "forgiven" and the child would be accepted into the higher caste.
Note: I am using the science-in-society tag because it deals with "questions about the use and perception of science by the inhabitants of a fictional world" and "asks how people treat and use science in-world." Seems appropriate here as I wouldn't consider this science-based (it's more of a creative thinking question than a science question). I would appreciate answers based in science but I'm not limiting answers to scientific ones.