Based on a review of the three-phased unfolding of the Atlantic Revolutions, what are two most important changes that were brought about to the Atlantic world?

The French Revolution (which began in 1789) and the Haitian Revolution (which began in 1791) were greatly influenced by the American Revolution (1775–1783).
That being said, the Atlantic Revolutions were actually a series of worldwide uprisings that occurred during the eighteenth and nineteenth centuries. Besides the American, Haitian, and French revolutions, there were revolts in Latin America (with Peru, Chile, Bolivia, Argentina, and others seeking independence from Spanish rule), Scotland (the Jacobite Rebellion of 1745), and Ireland (Irish Rebellion of 1798).
Now to get back to the French, Haitian, and American revolutions: these revolutions were mainly inspired by the Enlightenment, whose ideas about liberty, equality, and religious tolerance were the driving force behind the uprisings. Prior to the Enlightenment, kings ruled by divine right.
According to this doctrine, kings or monarchs received their power from God. Therefore, they were not accountable to the people. Instead, a king had absolute power, so all state, legal, and social institutions were subject to his authority. In that light, disobedience was considered treason and punishable by death. Certainly, anyone who dared rebel against his king was said to be in danger of hellfire. Meanwhile, the Enlightenment was all about ending this arbitrary divine right of kings.
The American Revolution, which inspired both the Haitian and French revolutions, brought new changes to the Atlantic world. Arguably, two of the most important changes were:
1) Absolutist regimes were overthrown around the world. In the United States, the new constitution provided for a system of checks and balances and a new Bill of Rights. In Ireland, the Irish fought to topple English rule and to gain religious freedoms. Please refer to my links above to read more about monarchical regimes that were overthrown during this time. You can also do your own research about the Latin American revolutions.
2) Both the American and Haitian revolutions heralded the beginning of a global fight to abolish slavery. Specifically, the American revolution led to the formation of the first abolitionist organizations in North America, such as the New York Manumission Society (1784) and the Pennsylvania Abolition Society (1775). As for the Haitian revolution, it eventually became known as the largest and most successful slave revolt in the entire Western hemisphere. Please refer to my link to read more about the Haitian uprising.