Docs, could a child who has had the mmr vaccination still get the mumps?

Yes: Recent imported cases from overseas to the houston area were found to have infected some who had received only one dose of vaccine. Protection for up to 85% is accomplished with the first dose and the 2nd dose brings it up to 95% or more. Any unvaccinated kid is at high risk as long as international air travel can bring it in to the country during a contagious phase.