If you are immune, then the MMR should do nothing for you. If you are not immune, you may now very well be "infected" with the vaccine virus and you'd just mount an immune response like someone who got vaccinated (or coughed at by someone with M, M or R).
As for DS - did he get at least some of the content of the shot? If yes, he should be making antibodies just fine. Since there are "live" viruses in the vaccines, they'll just need half a day more to get to the numbers that alert the immune system. Have you talked to the GP?