If one is having sexual relationship with minor (protected by parents) and parents disapprove the relationship, that is breaching of the third precept. What if an adult child having a (sexual) relationship with someone without the consent of their parents, of course everyone has their rights, but the question is is this breaking the third precept?
It depends on what the society consider as an adult. Back then in India, women always had a guardian regardless of their age. But things are quite different nowadays. In most countries when one reaches 18+ the society consider that person as an adult that no longer requires guardianship. Any care given after that is optional and any care accepted after that does not make one a minor, unless there is such an understanding between the 2 parties. In other words, when you become an adult by law, if your parents continue to give you food and lodging with the mutual understanding that you will not be sexually active with someone without their permission, it breaks the 3rd precept.
I think the question is invalid and the precept is redundant/obsolete.
The precept was spoken in the context of the other moral directives, such as parents arranging the marriage of their children (DN 31).
In current contemporary Western or Cultural Marxist societies, the precept is redundant and, if possible, would best be redefined.
For example, Thich Nhat Hanh has redefined the The Third Precept as follows:
Sexual expression should not take place without love and commitment. Be fully aware of the sufferings you may cause others as a result of your misconduct. To preserve the happiness of yourself and others, respect the rights and commitments of others.