First find out if the child in question has the chickenpox. If he doesn't then your child likely contracted them from being out in the community too. I know the chicken pox vaccine has changed and is more effective than it used to be so there is a chance the few spots he will get will be missed.

There is really no way to stop this kind of thing from happening other than to have kept your 2 month old away from anything to do with the daycare and taken extra precautions yourself when holding such as always putting a clean blanket on your shoulder and washing hands before touching.

The incubation period for most childhood diseases is anywhere from 2-4 weeks and there is no way to exclude a child that long for every possible exposure they might have had. Schools don't even exclude a child with chicken pox anymore in most cases like they used to although a child usually needs to stay home because they feel sick.