Was the Monroe Doctrine meant to serve as a vote of confidence and support for the new Latin American nations or was it meant to secure U.S. dominance in the Western Hemisphere?
It was definitely meant to do both.
When the Latin American countries started to win their independence, many in the US were very pleased. They saw it as a blow against monarchy and for democracy. They felt that the Latin American revolutions were based on the US revolution. The issuance of the Monroe Doctrine came about in part because of talk among European nations of retaking the new countries for Spain.
However, there was a desire for dominance in the Monroe Doctrine as well. The US refused to declare the doctrine jointly with Great Britain. Instead, it insisted on declaring the doctrine unilaterally. This shows that the US was trying to show its power and importance, not just to protect and support the newly independent countries.