There is no basis for this prescription in the authentic sources of Islam; it is important for us to know that in Islam no one has the right to prescribe religious duties without the sanction of Allah and His Messenger. I should also point out that attributing such things to Islam is akin to committing shirk: Allah says, Hence, do not utter falsehoods by letting your tongues determine [at your own discretion], "This is lawful and that is forbidden", thus attributing your own lying inventions to Allah: for, behold, they who attribute their own lying inventions to Allah will never attain to a happy state!" (Qur'an: 16:116).

Based on this, as Imam Ibn al-Qayyim has stated, prescribing religious duties based on one's own opinion without sanction of revelation is shirk.

It is, therefore, your duty to learn your religion from the right source.  

In conclusion, your mother does not need to offer any nafl at the conclusion of her 'iddah unless she chooses to do so, out of her choice, as nafl can be done any time; it is left to a person's discretion.