I was pressed by my Executive VP about my commitment to may large family and if I could travel

I have a 21 career with my large employer. Was told directly by my VP manager that he had to post a job similar to my position because of an HR political reasons, wanted me to go through the process of interviewing, but that I would get the job. When interviewing our EVP pressed me about my family situation (6 kids 2 with Down syndrome), and questioned if I would be able to commit to the international travel. In the end they hired a female employee who was no longer wanted in another business. Our company has no women in executive positions and HR does not want to let any go, but she had a history of poor business performance. My career has ended with the decision, I feel that the female HR placement was forced, being told I had the position put me at a disadvantage "interviewing", and the my family situation was an influence of the EVP. I earn over $300k per year and the company is a $2B publicly traded company. Is there a case?