Is it permissible for a woman to separate the performance of Sunnah and Fard prayers within a single prayer with a time interval to attend to her needs?

There is no harm in separating the supererogatory (Sunnah) prayer from theobligatory (Fard) prayer. Indeed, some scholars have even recommended it. The time for the supererogatory prayer extends from the beginning of the time for its associated obligatory prayer until its end.