When Protestants baptise their infants, they do so validly but illicitly. Every time they do so they incur damnation upon themselves because they do so out of disobedience to lawful Church authority--- that is to say, the Magisterial authority. The reason as to why they can't be re-baptised is because we believe in only ONE baptism, and the Catholic Church does hold that they baptise correctly even if illicitly.
Also, while their children ARE technically being baptised into the Catholic Church regardless of whether or not the people baptising them believe that, once they reach the age of reason they are likely automatically outside of it because of the years of indoctrination and their identity as Protestants. Even 1 mortal sin will send their child straight to Hell. Simply praying that Jesus will save them is useless because their religion bears no grace. They would need very deep and true contrition and a very special grace from God to be able to be saved from their imminent demise.
Also, you may want to note that children under the age of reason do not need to profess any faith. They can't profess any faith because there's no way they can understand it without the use of reason. This is why we have baptismal sponsors. To profess the faith on behalf of the children.