I'm afraid the new pics and information have not eased my concerns. The dollar should weigh 26.5 grams; anything 26 grams or less would be suspect.
The other side (I don't know which is reverse or obverse)
The pic in the top post is the obverse; it reads (in order top-bottom-right-left) Xian Feng tong bao. "XianFeng" is the reign-name for the emperor who ruled from 1850 to 1861 and literally means "all abundance" or perhaps more liberally, "plenty for everyone". "Tong bao" means "current coin". This is the standard obverse inscription for this emperor, seen on most
cash coins of his reign except for the large multiple cash (which typically used "zhong bao" or "yuan bao" instead).
On the other side, it reads (again, in the order top-bottom-right-left) Tian xia tai ping, literally "Heaven under great peace" or more grammatically, "Peace under Heaven". This is a formula not used on ordinary Imperial money, but was one of several forms used on palace coins.
However, I think it is extremely unlikely that this particular emperor would have issued coins with this particular wish expressed on his palace coins. That's because, for most of his reign, the forces of the Taiping Rebellion occupied most of southern China. Taiping Rebel coins use an obverse formula
very similar to this reverse, namely "Tai Ping Tian Kuo" (Great Peace Heaven Kingdom, or Heavenly Kingdom of Peace). The phrase "tai ping" would probably have churned the stomach of this emperor and he would not have wanted to put it on his palace coins. The palace coin of this reign illustrated in Krause is unique in using the phrase "Yi tong tian xia", meaning "One Unity Heaven Under" or "United Under Heaven". Reunification rather than peace was certainly the goal of the Qing Emperors until the rebellion was finally crushed in 1864.