。
She takes pride in her driving skill.
Literal
She [topic-は] her own driving's skill [object-を] pride [as-に] is-doing.
腕前 ('skill, ability, prowess') uses 腕 ('arm') in its productive figurative sense as 'skill' (the same body-part metaphor underlies 腕がいい 'skilled'); 前 here is a noun-forming suffix. The compound carries a flavor of mastery — not just being able to do something, but doing it with practiced finesse. 誇りにしている applies the [X]を[Y]にする pattern to take her driving skill as a source of pride.