Does the prayer become void if the worshipper unintentionally utters the word "Mama" when his daughter falls on the prayer rug during prayer, and is it permissible to continue the prayer after moving away the child who fell asleep or played on the worshipper's lap?

Speaking inadvertently during prayer, if it is minor, does not invalidate it according to the majority of scholars. Therefore, your prayer is valid, as is moving the child away from you. However, a Muslim should not allow their prayer to be exposed to distractions that prevent them from achieving devotion in it, because some scholars believe that excessive actions during prayer invalidate it.