If the matter is as described, there is no sin on your mother – if we assume that there is any sin involved – because she did not consent and the operation was done without her knowledge.
If trustworthy doctors determined that leaving the foetus inside poses a danger to the mother’s life, it is permissible to abort it, even if that is after the soul has been breathed into it.
It says in Ahkaam al-Janeen fi’l-Fiqh al-Islamiyyah by ‘Umar ibn Muhammad ibn Ibraaheem ‘Aamir:
The fuqaha’ of the Sunni madhhabs are unanimously agreed that it is haraam to kill the foetus after the soul has been breathed into it – i.e., after 120 days since conception – and it is not permissible to kill it under any circumstances, unless continuation of the pregnancy will lead to the mother’s death.
Thus it is clear to you that abortion after the soul has been breathed into the foetus is a crime and it is not permissible to do that except in cases of extreme and definite necessity, not assumed or imagined necessity, if it is proven that there is such a necessity, i.e., if leaving the foetus will pose a danger to the mother’s life. However it should be noted that with the advances in modern medicine and the means available nowadays, abortion to save the mother’s life has become something very rare indeed. End quote.
The Islamic Fiqh Council stated that if the pregnancy has reached 120 days, it is not permissible to abort it, even if medical examinations show that the foetus is deformed, unless it is proven by a council of trustworthy, specialist doctors that continuation of the pregnancy will pose a danger to the life of the mother. In that case it is permissible to abort it, whether it is deformed or not, so as to ward off the greater of the two harms. End quote.
The Council of Senior Scholars in the Land of the Two Holy Sanctuaries issued a statement in which it says:
After the end of four months it is not permissible to abort the foetus unless a number of trustworthy specialist doctors decide that leaving the foetus in his mother’s womb will cause her death. That is after exhausting all means of trying to preserve his life. The concession allowing abortion in this case is only allowed in order to ward off the greater of the two harms and serve the greater of the two interests. End quote from al-Fataawa al-Jaami’ah (3/1055).
See also the answer to question no. 42321.
And Allaah knows best.