I think attorney is a bit far fetched since Joshua was not an attorney. You apprenticed with your father or were a clerk in someone's law firm. It's more then likely he was being prepped to take over the family shipping business. You would have to have knowledge of contracts and such to conduct business.
There are many aspects to running a shipping business. Ships, ports, port workers and ship crews, types of goods being shipped and their shipping requirements, insurance (yes Lloyd's was around then), clients, customer relations, claims, ship wrecks and damaged goods, spoilage of goods, and blah, blah blah.
A few executives or managers would be needed to be on top of things with the slow communication of the day. It was a family business and the men would have all been needed. With Barnabas the only son of Joshua, he would have ultimately been the heir apparent. However, I believe this task utimately fell to Daniel when the others were killed off or indisposed in their coffin.
I am also basing this musing on the fact that Barnabas did not take up Victoria's defense but instead asked his Judge friend (who turned down the case) and then Peter Bradford. He was good at arguing the Constitutional law "she is innocent until she is proven innocent" and would have been a fine lawyer had he choosen that career path.
If they were anything at all, I do think the family may have been Federalist. George Washington was one as was Alexander Hamilton. Alexander Hamilton was very important to the merchant class with credit, national bank, etc. The old Democratic-Republicans were more for farming. They needed a strong credit system, banks, etc.
