My mother is right in the middle of preparing dinner.

Literal

Mother [topic-は] dinner [possessive-の] preparations [object-を] is-doing-[in-progress-ところです]

~ているところです = 'is right in the middle of doing X.' ところ adds temporal precision: not just 'is doing' but 'is at the point of doing (right now).' More immediate than plain ている.