My mother innocently asked, 'Would you like some more beer?'

Literal

Mother [topic-は] innocently [even-も] 'more beer [object-を] partake [question-の]' [quotative-と] asked

召し上がる is keigo (honorific) for 'to eat/drink' — 食べる/飲む elevated to show respect to the guest. The の at the end of the quoted speech is the feminine/soft question particle. 無邪気にも = 'innocently (even)' — も adds a nuance of 'of all things, innocently.'