First, welcome to the forum. Second, don't give up on us. There are some here who simply can not accept someone telling them that what they think can't be true. If you say the coin is copper through and through then that should be accepted until proven or shown otherwise. Are there any coin dealers in your area? It should be looked at by someone experienced in what coins should look like. The standard weight of a clad dime should be 2.27 grams. I'm not sure what the weight tolerance is but 2.25 grams is only .009% light so it doesn't seem too far off specs. It is possible that it was struck on a copper planchet intended for another country's coin. Is it 17.9 mm diameter?
According to Breen's Encyclopedia, the weight should be 2.268 + or - .09. Yours is well within normal limits. Missing clad layers would lower the weight substantially.