My mother went to great trouble preparing dinner for the guests.

Literal

Mother [topic-は] guests [possessive-の] dinner [object-を] prepare [nominalizer-の] [to-に] greatly went-to-trouble

骨を折る (ほねをおる) = literally 'to break bones' = to go to great trouble/make a great effort. 大いに = greatly. An idiomatic expression for extreme effort.