For civil courts, we are under British civil laws. Attorneys take the BAR, and an oath to the BAR: British Accreditation Registry. I’m fairly sure that the ABA falls under the BAR. This is basically a guild, as in the old European style.
Not sure what is “American Constitutional law”? Sounds like Common Law, based on the Bible, Declaration, Constitution, first 12 amendments. Practiced in SCOTUS.
I don’t think ‘American constitutional law’ is a real, legal thing, but ideally, all laws passed by congress would go before the supreme court to see if it abridges the Constitution and Bill of Rights. If it’s unconstitutional, then it gets squashed. If it passes the constitutional test, then it goes to the president to sign it into law or veto it. I feel that’s a good form of checks and balances.
Do they seriously swear an oath to an originally British association? No wonder there’s so much wrong with the government.