In principle, your children are either automatically Chinese citizens at birth or not, as a matter of law, and there is no "option" (other than to renounce Chinese nationality if they have it). In principle, if they are Chinese citizens with dual nationality, they cannot get Chinese visas, and the Chinese consulate will issue them Chinese Travel Documents, which are passport-like booklets in which it says the bearer is a citizen of the PRC, valid for 2 years. If they are not Chinese citizens, the Chinese consulate will issue them Chinese visas, and they cannot get Chinese Travel Documents.
According to Article 5 of the PRC nationality law, the children born abroad are Chinese citizens at birth if at least one parent is a Chinese citizen at the time of their birth, unless at least one parent is a Chinese citizen who has "settled abroad, and the children have foreign nationality at birth. At least one parent (your wife) was a Chinese citizen at the time of their birth, and they do have foreign nationality at birth, so it hinges on the condition of whether there is a parent who is a Chinese citizen who has "settled abroad". Your wife is the only Chinese citizen parent, so it depends on whether she has "settled abroad", which has been interpreted by the Chinese government as having foreign permanent residency. If your wife had foreign permanent resident status at the time of the child's birth, the child would not be a Chinese citizen, but if she didn't, the child would be a Chinese citizen (and would continue to be one even if your wife obtained foreign permanent residency or even foreign citizenship after the child's birth). You have not provided enough information to determine whether this is the case.