。
She doesn't mind doing chores.
Literal
She [topic-は] miscellaneous-tasks [object-を] do [nominalizer-の] [object-を] does-not-begrudge.
いとう ('to begrudge, resent, dislike') is a slightly literary verb usually appearing in the negative いとわない — 'doesn't mind X, doesn't shy away from X.' A nice expression of willingness without enthusiasm. Pairs with disagreeable tasks: 苦労をいとわない ('doesn't shy from hardship'), 危険をいとわない ('not deterred by danger'). 雑用 ('miscellaneous tasks, chores, errands') is the noun for assorted small jobs, written 雑 ('miscellaneous') + 用 ('use, business').