"To suppose arms in the hands of citizens, to be used at individual discretion, except in private self-defense, or by partial orders of towns, countries or districts of a state, is to demolish every constitution, and lay the laws prostrate, so that liberty can be enjoyed by no man; it is a dissolution of the government. The fundamental law of the militia is, that it be created, directed and commanded by the laws, and ever for the support of the laws." -- John Adams
Read that again carefully. It does not say what you think it does.
Of course our use of arms is managed by law. Nobody contends that anyone should be able to do target practice on a city street, or shoot clerks who ring up wrong bills. We are, of course, to act within the law, and to use arms outside the law will quickly destroy law & society - which is PRECISELY why gunowners are such a remarkably law-abiding bunch: they understand the power of arms.
Adams' admonition to use arms only for self-defense, or in service to a jurisdiction, presupposes personal ownership of arms: one cannot very well use a pistol for self-defense, or a rifle to protect the state, if one has neither pistol nor rifle. The only reason I can defend myself is my posession of a pistol, and the only reason I can move to the front line in defense of my state within minutes is my ownership of a rifle - and that I have trained with these very tools. By opposing personal ownership of arms, you not only prevent what Adams says one should not do, but also prevent what Adams says one _should_ do.
Our governments have taken your approach and gutted Adams' words: by banning arms (on the whole) and failing to organize & train those with arms, citizens cannot defend themselves or their state - actions which Adams noted were reasonable and expected. If you expect me to stop my would-be murderer, I must have a pistol. If you expect me to act in defense of my state, I must have an M16 and appropriate training. I will pay the costs out of my own pocket, and spend my own time preparing - but if the state forbids my ownership of arms and related training, the state cannot expect anything of me when I am called to defend the state. I cannot give that which I am not allowed to have.
John Adams never advocated that citizens be disarmed; in your quote he simply advocated that citizens obey the law while they posess arms.
Correction: when they use arms.
Essentially what Adams is saying is that citizens should only use arms [against other people] for self-defense, or as directed by the government; they are not to act as non-governmental vigilantes. For citizens to use their arms in vigilante actions would be to undermine even a fully-legitimate government.
To be sure, John Adams fails to recognize what should have been additional non-governmental uses for weapons (e.g. hunting, practice). He also fails to recognize that use of arms against lawless government personnel may need to extend beyond individual self-defense (e.g. Battle of Athens, ca 1946 or so). Even he, however, did not come anywhere near implying that citizens shouldn't possess arms or be able to use them in their own defense.