Part XV of the UN is responsible for settling disputes.
The Majority Leader is the highest ranking member of the party in the Senate that has control of the Senate. Their number #2 is the party whip, who is responsible for handling vote counts and ensuring that the party votes as a unified block.
John Cornyn of Texas is the current Senate Majority Whip.
This would be called Island Hopping. This is the slow process of capturing one island after another.