My 70 year old mother is recovering from surgery to fix a broken hip. How can I help her become independent again?

Encouragement. You can help by keeping her spirits up and encourage her to move and to walk. However, this will take time (sometimes 12 months) and the number of patients who will regain functional independence is usually about 50% with most patients losing one grade of activity (i.e. If prior to fracture, she was a community ambulator, she will likely be a home or limited community ambulator).
Patience. Recovery from surgery for a hip fracture can take up to a year, with a significant proportion of patient regressing in their ambulatory status compared to pre-op. Help her progress through physical therapy.