What does 'official legal tender' mean?
Widely used and accepted as payment in the thirteen colonies, the United States government gave them (Spanish Silver Dollars) the status of
official legal tender.

I'm not clear about the meaning of 'official legal tender'. What does it mean?

Besides, the structure of the sentence does not make sense. I suppose the logical subject of the past participle phrase should be Spanish Silver Dollars.

Could I rewrite the sentence like ' Widely used and accepted as payment in the thirteen colonies, Spanish Silver Dollars were given the status of official legal tender by the United States government? Thank you.

Question

What does 'official legal tender' mean?
Widely used and accepted as payment in the thirteen colonies, the United States government gave them (Spanish Silver Dollars) the status of 
official legal tender.

I'm not clear about the meaning of  'official legal tender'. What does it mean?

Besides, the structure of the sentence does not make sense.  I suppose the logical subject of the past participle phrase should be Spanish Silver Dollars.

Could I rewrite the sentence like ' Widely used and accepted as payment in the thirteen colonies, Spanish Silver Dollars were given the status of official legal tender by the United States government? Thank you.

Answer

Official legal tender means the government said that these coins could be used to pay all legal debts.  So if you owed somebody or some company money, you could pay off that debt with those coins and a court would rule you had paid your debt. By making the coins "legal tender" it would encourage businesses and people to adopt their usage and turn that usage into a common occurrence.  Both sentence structures sound fine to me.

Answer

Legal tender is a medium of payment allowed by law or recognized by a legal system to be valid for meeting a financial obligation.

I agree that your use of the words in the sentence sound correct.