@boomerang,
It depends on whether or not the kids have any kind of serious allergic reaction to the vaccinations.
As a kid, I had a serious reaction to the polio vaccine and passed out in the parking lot as we were exiting the medical center. I was always told to only receive the polio vaccine using the sugar cube method.
As an adult, several times I've had a stronger than mild but not severe reaction to flu vaccines. So much so, that I refused to get them for many years because I felt I always ended up with a worse case of flu immediately after getting the injection.
After moving in with BBB two years ago, I gave in and got a flu shot since I was going out in the public a lot to do errands and didn't want to bring anything home to BBB. BBB and the pharmacist/nurse both insisted there wasn't any live viruses in the vaccines and it was all in my head. I got the injection and a few minutes later, I started feeling dizzy, sweaty and had a rapid pulse. They made me sit there for half an hour to make sure the reaction subsided. Turns out, I'm allergic to an ingredient used in the vaccines. We suspect it is tamiflu but no one knows for sure.
As far as I know, I've had all the vaccines for the common child hood diseases such as chicken pox, measles, mumps, etc., and didn't have any reaction to those. I've also had the diseases themselves and have built up immunity that way.