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Praise be to Allah.
First:
It is not permissible to amputate a healthy limb due to suspicion that it may become diseased in the future as this is a form of transgression against that which Allah, the Exalted, has created and is not necessary.
Sh. Ibn ‘Othaimeen said while establishing the obligation of circumcising males: “It entails cutting a part off the body, and cutting something off the body is impermissible, and the impermissible cannot be allowed without it being an obligation.” End quote, Ash-Sharh al Mumt’i (1/166).
You should place your trust in Allah and take precautionary measures.
Second:
As for the breast affected by cancer, then if there is no way to cure it and escape its danger except through removing it, then removing it is allowed. This is so due to the great need or necessity and to prevent the sickness from spreading to other parts.
Dr. Muhammad ibn Muhammad al-Mukhtar ash-Shinqiti (may Allah protect him) said: “One of two cases apply to these tumours:
The first case: They are restricted to one region, such as:
1.Colon cancer
2.Primary malignant liver tumours
3.Malignant breast tumours
4.Testicular cancer
5.Rectal cancer
In these cases, removal is a successful remedy to cure the patient and save him from the harm of these tumours, with the permission of Allah. So it is permissible for one to do this due to the great need, which may reach the level of necessity. And Allah knows best.” End quote, Ahkam al-Jirahah at-Tibbiyyah (pg. 315).
Third:
It is permitted to have an artificial breast implant to replace the removed breast.
From the resolutions of the Islamic Fiqh Council on plastic surgery we find:
The International Islamic Fiqh Council, belonging to the Organization of the Islamic Conference, in its eighteenth session in Putra Jaya (Malaysia) from 24-29 Jumaada al-Aakhirah 1428 AH (9-13 July 2007 CE) has declared the following:
After studying papers on plastic surgery and its rulings sent to the Council, and after having listened to discussions on the matter, the Council declares:
It is legally (Shari’ah) permissible to undergo plastic surgery out of necessity or need if the following is intended:
1.To return the condition of the limbs back to the way they were created as per the saying of Allah (in meaning): “We have certainly created man in the best of stature;” [95:4]
2. To restore normal function back to the limb/ organ.
3.To correct birth defects such as: a cleft lip, severe crookedness of the nose, abnormal birthmarks, extra fingers and teeth and joined fingers if their presence would lead to significant material or psychological harm.
4.To correct sustained defects such as those caused by fire, accidents, diseases and so forth. Examples of such procedures include: cultivation or transplantation of skin, partial or complete reconstruction of the breast, and hair transplants, especially for women who have lost their hair.
5.To rid oneself of disfigurement which causes psychological or physical harm. End quote.
See also questions 138273 and 146289.
And we ask Allah to make you well and protect you from every harm.
Important note:
It says in the question: “The doctors have told me that they have found a genetic fault in me… and they therefore believe that we carry a genetic fault in our family”. If by that they mean they found some fault or defect in these genes, then this may happen to some people and it is a test, like other tests which Allah decrees for His slaves for some wisdom.
However, if their intention is to accuse the Creator of an error or the inability to create a normal gene then this is great disbelief in Allah, the Exalted. He is capable of all things, and His actions are based on wisdom; they are elaborate to the highest degree as He, the Exalted, says (in meaning): “[It is] the work of Allah, who perfected all things.” [27:88]
And Allah knows best.