She feels at ease at their place.

Literal

She [topic-は] their [genitive-の] house [at-に] is [when-と] relaxation [object-を] feels.

The conditional/temporal と here means 'when, whenever' — it links a stable cause to a stable effect, often used for habitual or general truths ('when X, Y always happens'). ~にいる ('be at a location') uses に for static existence in a place. くつろぎ is the noun form of くつろぐ ('relax, feel at home'); 感じる takes the felt thing with を. The whole sentence lays out a routine fact about her ('at their place → relaxed') rather than describing a specific moment.