Visa application submission location and payment details

Hello. We are bringing our family of 8 (2 parents and 6 children) to Beijing and Xian for 4 days while we tour Asia. Because it is already costing a lot for 8 entry permits, we are trying not to use an agency for added fees. My son and his wife live in Chicago and they can take our applications to the Chicago embassy. Is this all right if we live in Utah, USA, that my son takes the applications to the Chicago consulate? Also, could you please tell me how to send the payment with them? Do you accept a personal check or money order, and to whom to we make the check payable? Or should we send cash? I don't think we should have any problem with the entry permits if we fill out our forms, and have already bought plane tickets to Beijing and from Xian, and train tickets, and hotels. Could you give me reassurance that we will probably get our entry permits just coming as a tourist family? Thank you very much for your help. If you have other advice for filling out many forms, I am happy to read it.