And re your points - don't forget the difference between de jure and de facto, and between realpolitik and ideals.
Whether you think a government is a good or morally right one is a different question from whether it is the lawfully constituted government of the day. Perhaps it would help to look at an OT eg - Mr Mugabe is the legal government of his country. To go to war against him is to rebel against that authority. It might strike you as a good idea to do so, but that is what you would be doing.
There are various ways in which a de jure government can be formed - elected, inherited, by force of arms, etc. One of the ways in which its legality is determined is by its recognition by other nations. That in turn governs the conduct of other nations. That's why, for example, countries have at various times recognised (or not) Taiwan, Communist China, East Timor, etc etc. Basically, if no-one else recognises you, you're probably not the legal government.
International law used to be called "The Law of Nations" which in many ways I think was a more useful name.
Cheers
C