Word for “place of power”

"Powerhouse" could render what you are looking for.

(Cambridge Dictionary)
country, organization, or person with a lot of influence, power, or energy:
♦ Germany is an economic powerhouse.
♦ The university is no longer the academic powerhouse that it once was.
♦ She's a powerhouse of original ideas and solutions.

• The stage was her powerhouse, where she felt as if she could conquer the world.

(ref;) At home , in the kitchen that was her powerhouse , centre of strategic planning and theatre of operations , Yvonne Kelly was having a fit of stove rage.

I immediately thought of "genius loci" but I don't think that applies here so much? Locus (of control/power) might work in the same vein, but I am not so sure the more I think on it. I agree with the use of dominion and domain in any case, maybe a similar word like turf or zone could be used instead.

Cathedral

The stage was her cathedral, where she felt as if she could conquer the world.

Used literally, a cathedral is where the Bishop's throne (or cathedra) is located. Used figuratively, it can be an important location of authority or power, with connotations of religious contemplation or being closer to the divine.

To Susan, an art gallery was her cathedral, her sacristy, her confessional, and her life’s work. (Source)

A place of power can be called a citadel.

Bastion suggestive of power

Also stronghold

Or zenith

Bailiwick