Was Manifest Destiny justified or was it our right as Americans to go from "sea to shining sea"?

This is really not an either-or proposition.  The idea that it was the right of Americans to spread from “sea to shining sea” is essentially the same thing as Manifest Destiny.  So, we cannot really set these up as two different options.

In my view, we cannot justify Manifest Destiny in terms of our modern moral values.  However, it was justifiable in terms of the values that practically everyone held in the mid-1800s.  In those days, there were very few people who objected to the idea that “might makes right.”  People pretty much assumed that strong countries had the right to conquer weak countries.  The Mexicans, for example, lost much of their land to the US in the Mexican-American War, but they had no problem with the idea that it was acceptable for them to take that land from the indigenous people who lived there.  This was a time when countries regularly fought wars to try to gain more territory.  Therefore, the idea that the US was strong and was therefore destined to spread from sea to shining sea was perfectly justifiable given the way people thought in those days.

Today, of course, we think differently.  We think it is terrible for a country to take land from another country just because it is strong enough to do so.  In this way of thinking, Manifest Destiny is absolutely wrong.  It is tantamount to saying that a strong person has the right to steal from a weaker person.  However, in the mid-1800s, this was not how people thought.