Chinese Coin?

Alas, your suspicions are confirmed. It's a reproduction. The Chinese have been reproducing these for decades, so it's not at all surprising that a fake has become a family heirloom. We can offer your customer several reasons why their coin is not genuine.

First, is the coin itself. This coin was not actually issued for circulation; it's a "pattern", issued to test and seek government approval for a design that was ultimately rejected by the government. As such, there aren't very many of them. The coin is listed in the Kann catalogue of Chinese dollars as number 212; do an Internet search for "Kann 212" and you'll find several pages featuring genuine examples to compare your coin with, such as this one on NumisBids from a 2013 auction in Hong Kong. It sold for US$5500, so as you can see genuine ones are rather pricey. All of this makes it extremely unlikely that a Chinese dollar randomly picked up from the streets decades ago is going to be a genuine pattern dollar.

Second, there are stylistic problems. The details are weak and "mushy", particularly in the centre of the reverse (Chinese-only side) and the leftmost Manchu word at 11 o'clock has virtually faded away. This effect is very commonly seen on counterfeits, where the dies used to make them have been weakly transferred.

Third, the "railroad rim" of the obverse, the sharp extra border right around the entire edge of the coin, is also very distinctive of mass-produced Chinese fake dollars. This is put there by the ring die these coins are forced through to give them a reeded edge. Genuine coins are not made using a ring die, but a collar die in the press as the coin is being struck. Many fake-makers try to file off the telltale railroad rim in an effort to hide this well-known defect, so a coin with fully rounded-off corners is also cause for suspicion.

Finally, can I suggest you weigh it. From all appearances, it is not a high-quality numismatic forgery, so it's pretty certain the weight is going to be wrong. I predict it will weigh several grams less than the 26.9 grams it is supposed to weigh. You could also try the good ol' magnet test; it might even be a steel fake. Whatever it's made of, it almost certainly won't be made of actual silver.