My mother asked me to prepare the meal.

Literal

Mother [topic-は] me [to-に] meal [possessive-の] preparation [object-を] do-[request-てくれ] [quotative-と] asked

してくれと頼んだ = 'asked to do (for her).' てくれ is the plain imperative of てくれる, here softened inside a quoted request with 頼む (to ask/request).