Every day except Sunday, she visited the hospitalized elderly man.
Literal
She [topic-は] Sunday [object-を] [excluding-除く] every-day, [hospitalized-入院中's] that elderly-person [object-を] visited.
~を除く ('excluding ~') used as a noun-modifier — 日曜を除く毎日 literally 'every day excluding Sundays.' This patterns alongside the alternate 日曜日以外、毎日 (using the noun-suffix 以外, 'other than'): same meaning, different grammatical packaging. 入院中の serves as an adjectival modifier ('hospitalized') from the noun 入院中 + の.