Is it permissible for a mother to spend her iddah (waiting period) after her husband's death in her son's house in another governorate 13 hours away by travel, knowing that she began her iddah in her original governorate?

It is not permissible for a woman who has moved to complete her iddah (waiting period) in her (new) home. Rather, she must observe the iddah in the home where her husband passed away while she was in it. It is not permissible for her to move from it unless there is a necessity, and the duration of the iddah is calculated by lunar months.