My mother stood with her hands on her hips and elbows out.

Literal

Mother [topic-は] both-hands [object-を] hips [to-に] placed elbows [object-を] spread was-standing

A vivid posture description. 両手を腰に当て = 'placing both hands on hips' (当てる = to place against). ひじを張って = 'elbows spread out' (張る = to stretch/spread). たっていた = 'was standing' (casual ている contraction).