Your core ray is not inherited from your parents. Parents try to teach their children and guide them towards what they believe will make them happy. Unfortunately, the children have a good chance of being from a different ray than the parent and therefore have different requirements for happiness.
It is possible to inherit issues from your parents if they have any unresolved issues at the time of their death. The ray that embodies that issue then has to be worked through as it surrounds your own core ray.
For example, Bill has an issue where he feels the need to always be the provider for his household. The issue comes from the blue ray. When he suddenly passes away without resolving the issue, his daughter Candace finds herself in a life altering situation. Her core is green and she has the dream of becoming a singer. With the passing of her father, she feels the need to start working at an office instead because she feels that she needs to be a provider for her family. Candace now has to overcome that issue (blue ray) and then return to following her dreams (green ray) in order to be truly happy.
Every person is here to live an independent life and there are different form of happiness.