There are really two distinct questions here, but they are common.
- Is cancer heritable?
- Is cancer (or cancer risk) contagious?
- Most cancer cases are not heritable. Some are. Heritable cases have particular characteristics (early onset, more than one close relative, often with cancer at multiple sites).
- Cancer is not contagious. Some cancer risk factors are contagious.
Is cancer heritable?
As Knudson, who developed the two-hit hypothesis, liked to say Cancer is a genetic disease of somatic cells. This is related, but different in important ways from a genetic disease of individuals. Tumor cells are genetically distinct from non tumor cells in an individual with cancer. Though there are hereditary forms of most cancers, the great majority of cancer cases are not hereditary). That is to say, in most cases, the mutations that lead to the formation of the cancer are not inherited from a person's parents. A family history of cancer becomes significant to a clinician when there is an early age at onset in two or more close relatives (See Robbins and Cotran Pathologic Basis of Disease, Ch. 7). Often, these hereditary cancers involve multiple tumors (see the second Knudson reference above, as well as here). Relevant to the hypothetical case here, breast cancer in a woman in her 60s would not suggest a hereditary form a cancer that would be associated with a higher risk of cancer in the son. Breast cancer in a woman 45 or younger would make a hereditary form of cancer more likely, which would be associated with a higher risk of cancer in her son. There are other risk factors to be considered, though (e.g., multiple close relatives with breast or ovarian cancer, being of Ashkenazi Jewishish heritage, among others). Guidelines for testing for the involved genes are in flux.
In summary, in this hypothetical case, it is unlikely that the son is at higher risk of any cancer.
Is cancer or cancer risk contagious?
The general question here is complex. The specific question here can be answered relatively easily, though.
Here, the specific question seems to be: in a hypothetical scenario, given a mother with breast cancer, is there a risk of sexual transmission from the mother's son to his wife. The answer here is quite clearly no. As discussed above, the potential risk for the son here is that of a hereditary cancer syndrome. That risk is minimal, but if it wasn't, hereditary cancer syndromes are not transmitted horizontally through sexual contact.
The more complicated question has two parts itself:
a. is cancer contagious
b. is cancer risk contagious
Is cancer contagious?
Transmission of tumor cells from one individual to another happens, but is quite rare. Though tumor cells do metastasize in an individual, when this occurs, tumor seeds must be able to evade the immune system and find an environment suitable for adhesion and replication. Tumor associated cells (non cancerous cells that regulate the microenvironment to make it favorable for growth and replication) are discussed in this 2011 Hanahan and Weinberg paper. There are similarities to infectious processes, but cancer is not measles. Tumor cells don't shed in comparable numbers, aren't adapted for immune escape in a separate host, and don't express appropriate adhesion proteins for portals of entry on a new host or readily induce tumor associated niches in a new host. The cases where person-to-person transmission of cancer via tumor cell inoculation does occur seem to demonstrate more how cancer cells are not infectious agents.
Donor-related tumors in transplant patients occur in immunosuppressed patients, but are still rare. The low frequency of transmission seems to be due, in part, to screening. The fact that we see this at all demonstrates the significance of transmission route and immune escape.
Maternal-fetal, and in utero twin-twin seem to be exceedingly rare, but have occurred, again, demonstrating the existence, but poor efficiency of transmission
Inoculation of volunteers with tumor cells in a problematic series of experiments at Sloan Kettering in the 50s, transplantation of tumor cells into patients with other cancers, resulted in growth, recurrence after excision, and death in some cases. Transplantation into healthy volunteers (yes, they did this) resulted in nodules that spontaneously regressed. This experiment has since been interpreted as evidence for immune system control of transplanted tumor system in healthy individuals, as compared to growth and progression in a receptive niche in a cancer patient.
So person-to-person transmission of cancer cells is rare, seemingly because, unlike an infectious microbe, there is not a suitable receptor for adhesion at an exposed or accessible site, a suitable environment for replication, and adaptations for immune escape by tumor cells in the original host are not effective in a new host.
As a side note, there are contagious cancers in other species, but this doesn't seem to be particularly relevant to a question about whether cancer (or cancer risk) can be transmitted between two humans.
Is cancer risk contagious
17% of cancer cases worldwide are attributable to infectious agents (see Cecil Medicine, Ch. 183), these include viruses (e.g., HPV, hepatitis B and C, HIV, Epstein-Barr, and human herpesvirus-8) and bacteria (e.g., H. pylori). These are all contagious. At least somewhat related to the question, many of them are transmitted through sexual contact.