I have sent USD to Philippines (converted to PHP) using online WU, so am sure you can do it. You can also try taking USD to the local WU and try transferring that way (I have never sent USD to US through WU from the Philippines), I think they have a $10,000 limit per transaction. The only other feasible option there is to do what you mention, opening up a dollar acct at a bank that you can do wire transfer(s). Good Luck!!
From my recollection, and it is all a blur, I had a large sum of money (USD) from my husband's life insurance that I had to have deposited into our BPI dollar acct in Dumaguete. When I left for the states I had to have it all sent to an acct in Oklahoma I had my daughter open for me so the money would be here when we arrived. I had to use SWIFT code (similar to routing info, just ask your receiving bank for their SWIFT code. You can also check here, but I would verify with the bank : SWIFT Code for all Banks in United States). It didn't cost much for the transaction, but did involve quite a bit of paperwork.
Swift code is for sending money internationally. Kind of like a routing code, but for the world. BIC / SWIFT code for any bank and SWIFT code lookup - TransferWise
With all due respect, I doubt China Bank cannot accommodate a bank to bank transfer to the USA, unless your wife isn't authorized at the bank as account holder. I would strongly advise (your wife) to have another talk at the bank, preferably with the manager, in order to clear up exactly what the bank needs to execute the transfer (make sure she brings the correct SWIFT codes for your bank in the USA, ask your bank for those). Moreover, I would try to get a better than standard deal on the exchange rate from China Bank also.
I recommend this suggestion, some teller might not inform you about other things to do. Better to talk to a manager.