I’d suggest:

C’est mon refuge.

thus you can stick to one word while still keeping the idea of both feeling at home and wanting to be there.

Obviously, using c’ implies you’ve mentioned “her” before so that it is clear c’ refers to “her”. Can be adapted to whatever context you have.

Elle est mon refuge.

could be used depending on context, but be aware c’ is more idiomatic.

The notion of someone feeling like an emotional home to you sounds really weird. I am not sure I understand it well, so these may not correspond exactly to what you want.

You can say:

ma moitié

It is about the idea that people are not complete without their partner. You can only say that about someone you are already engaged with.

mon âme soeur

Equivalent to the English “soul mate”. Usually someone you are in love with, not necessarily engaged with.

mon havre de paix

It’s not an idiomatic way to speak about someone, usually it refers to a place, but it seems to be the closer to what you want to express. It means “a place where there is never any conflict”.