My mother absolutely never gets up early.

Literal

Mother [topic-は] absolutely early-rising [contrast-は] don't-do.

Watch the double は: the first marks 母 as topic, the second attaches to 早起き and turns it into a contrastive topic inside the comment — the negation is specifically about early rising, as opposed to other things she might do. Replacing the expected を with は in 早起きはしない is the structural move that delivers the emphasis; ぜったいに reinforces it.