You have rights with CPS. You don't have to agree to let them in. You can make CPS come back with a warrant, but they will do just that, and in the end, they will be allowed to come into your home and investigate, whether your wife wants them to or not.
CPS is an enormously powerful agency, and if they have received a report that gives them a reason to believe that a child is at risk because he's in an unsafe environment, the state allows them to swoop in and remove a child from the household.
CPS is notorious for pushing their weight around, for stepping all over parents' rights, and even for fabricating facts and evidence to support their findings. Even worse, judges tend to believe CPS.
So because of the power that the state allows CPS to have, in the end, when CPS wants to investigate you and your home what they want would come about one way or the other.
Most CPS complaints turn out to be unfounded. But they will be back to make sure because your wife didn't comply and if they have to go to court to get her compliance, they will.