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First law: every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force resulting from unbalanced forces acting on an object https://www.grc.nasa.gov/www/k-12/airpl ... ton1g.html
Newton's second law: F=ma is force, M is mass, a is the acceleration
https://www.google.com/search?ei=MaZRWo ... u4XLVvOD9g
a = F/m; if F = 0, then a = 0 too. That mean no acceleration, an object remains its current state. So, the first law and second can be united by the second law.
The question is: how can the third law be united with the first and second laws, particularly on the level of philosophy?
The third law is: every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard. http://teachertech.rice.edu/Participant ... /law3.html
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This is why in every phenomenon three forces are involved. The law was known in certain ancient systems and was called 'The Law of Three'. One force was called the active force. The force opposing or resisting it was called the passive force. The third force, which enables the active force to overcome the resistance of the passive force, was called the neutralizing force.
This law is unknown to modern science, hence the conundrum you've elucidated here. The third force is not known because it's hard to see. It's usually taken to be the medium in which the other two forces are acting, or as the result. So the Law of Three has not yet been discovered by modern science, and Newton's laws remain disunited.
For example, take the phenomenon of a baby being conceived through sex. In ordinary science, only two forces are seen, and a result. The two forces seen are the male and female principle, the yin and yang coming together in the act of sex, which results in a new human coming into existence. In reality the baby is the third force, without which the act of sex could not occur. The baby is destined to be born, or there is a force (desire) which is trying to make a new human be born, and this force is just as much a cause of the act of procreation as is the actions of the male and female in having sex.
When/if modern science ever discovers or learns about this principle of three forces, Newton's three laws, as well as many others, will be 'united'. But until then, as long as science only deals with two forces, action and resistance (active and passive), not only Newton's laws but many other things will continue to be apparently disconnected...
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As the OP says, the first law is really just a special case of the second law where force and acceleration are zero.
The third law combines with the second law (in its more general form), and therefore also with the first law, to result in the law of conservation of momentum. But, if by "united" we mean "turned into a single statement", I don't think it necessarily should be united with the first two laws. I don't think that's what physicists normally mean when they talk about uniting laws of physics. The idea of creating a theory of physics which applies to every possible physical system in the universe ("[grand] unification") is not necessarily about finding a single sentence which describes the whole universe. It's about finding a set of statements which are all mutually consistent.