The most important condition for a useful consultation is a quiet room where the doctor and parent can relax and sit together undisturbed by others.
Literal
Useful meeting [gen-の] most important condition [topic-は], doctor [and-と] parent [subj-が] relax-and, other-people [by-に] not-be-disturbed-[without-ずに] concerned-parties only-[で] sit [poss-の] able-to-do quiet room [copula-だ].
A long, complex sentence of the sort found in parenting manuals or clinical guidelines. Key structural features: 最も大切な条件 ('most important condition') as the topic, a multi-clause relative clause modifying 部屋 ('room'), including stacked adverbial clauses — くつろいで ('relaxed and'), 邪魔されずに ('without being disturbed'), 座ることのできる ('can sit'). 当事者 ('the parties concerned') is formal/legal vocabulary. The whole structure is Japanese-typical: heavy modifier, noun at the end.