Right, the law came through Moses, but Hagar's children represent those born slaves to the law. Everyone is born a slave to the law, until the times set by our Father and we are born again.
The law became our tutor to lead us to Christ(Gal 3:24). The word for "tutor" in that verse is actually pedagogue. The pedagogue did not teach, he only watched over the child's behavior. The child was put under the care of the pedagogue until they reached an age determined by the father.
So the law watched over our behavior until we became of age.
3:25 – When faith comes in, the responsibility of the law is removed.
The adult does voluntarily what he formally did in fear of the pedagogue, the law.
Keep in mind that the 2 women represent 2 covenants(Ga; 4:24)---law and grace. Judaism is a legalistic religion, but when our time comes we must do what Gal 3:30 says---cast out the woman and her son, the law with its many made rules, for salvation.
My bottom line is that we are born physically, we are slaves to the law for our salvation. . When we are born again, the law is no longer our means of salvation. We are not children of the bondwoman, but of the free woman---...therefore keep standing firm and do not be subject again to a yoke of slavery(the law)
I think you've got it all wrong, but there's no point in endless dispute. The metaphor of the bondwoman and her son, compared to the freewoman and her son, eludes to Jesus. Through Isaac Jesus came and "set you free" from the law, so that you no longer follow the law by a written code, but in a new way "by the spirit"