She somehow managed to back through the narrow driveway.

Literal

She [topic-は] that narrow driveway [object-を] somehow back-with passed-through.

ドライブウェイ is the kind of katakana loanword that betrays a relatively recent arrival — the everyday word 私道 ('private road') exists, but the loanword feels more specifically suburban, evoking American-style residential layouts where each house has its own driveway. Such layouts are uncommon in Japanese cities, where most parking is rented at separate lots or compactly tucked into narrow garage spaces, which is precisely why backing through one becomes a story worth telling. The path-を with 通り抜ける treats the driveway as the route the vehicle traverses.