I just went through this in deciding the criteria for people coming over this winter while we keep DS2 isolated. I'd decided that if anyone received flumist, they should give it at least a week before coming over. That's based on the package insert, which you can download
here. The insert includes the results of a study on transmission conducted in a daycare.
Quote:
| With documented transmission of one Type B in one placebo subject and possible transmission of Type A viruses in four placebo subjects, the probability of acquiring a transmitted vaccine virus was estimated to be 2.4% (95% CI: 0.13, 4.6), using the Reed-Frost model. |
Quote:
| Vaccine recipients or their parents/guardians should be informed by the health care provider that FluMist is an attenuated live virus vaccine and has the potential for transmission to immunocompromised household contacts. |
Interesting that it doesn't say just what that potential is, nor what precautions if any should be taken.

OP, in your case, I wouldn't be worried about your mom and grandmom. That's a degree of separation from the live virus itself. I'd guess that the health care workers they see who may be required to get the flu vax would have a much greater probability of passing it on to them than your DS.