The original German is 'der Wille zur Macht'
I think the original interpretation is correct.
Neitsche includes domination in his view of power, but he also includes influence and all other ways of affecting the world. Power, is at root, 'potesse' -- being able, and not necessarily oppression. In fact, he notes that oppression is too much directed at others to really be absolute power. In caring that you dominate, you give power to those dominated, whose responses actually determine your happiness.
His less didactic books, like 'The Gay Science' and even 'All too Human' have a focus on art as an aspect of life that makes no sense if one thinks of power as domination alone. Artists do not dominate, they influence.
And in fact, in his critiques of Wagner, he points out how, when art dominates, it actually has less power, because it loses the ability to influence on a more detailed level. Power aims to make the world exactly as one wishes it. This cannot be accomplished any better with a maul than with a paintbrush if the essence of your vision has a great deal of detail.
Nietzsche also has a vision of the unity of opposites that strongly foretells psychoanalysis (thus the need for a focus that questions values, as captured in Beyond Good and Evil). For instance, in The Gay Science, he admires the motive of domination so strong that it can be adequately served by forgiveness, being 'Drunk off' in imagination so deeply that it leaves one overly full, and calls for its opposite. He points out that doing good for others is also a way of controlling their lives. If you are powerful in a way that suits your nature, then, you might be magnanimous, or endlessly motherly, rather than dominant.
Here 'to' means 'for', 'toward' or 'unto'. Although 'zu' is also used with infinitives, like the English 'to', given the article marker and the capitalization 'Macht' here is a noun and not an infinitive. It is more often translated 'for' in such cases, to remove an ambiguity that exists in English and not in German. However, Schopenhauer's 'Wille zum Leben' had already consistenty been translated "Will to Live' rather than "Will for Life", and this naturally followed that compromised construction.