How was this able to happen? So what if Tony was in the hospital and Dick Barone dies? How was his son able to sale what was basically Tony's to New York? Just seems odd that Tony would allow his main source of legitimate income to be taken from him. Did I miss something that explains why this happened?

He was oblivious to the life or his father's association. He thought he was selling a business legitimately. He honestly didn't know to consult Tony or reach out to an associate.

The mother pleads with Tony not to hurt him and basically admits that he was a sheltered kid and moved from Jersey and had no idea what he was doing or the repercussions of his actions.

That being said it was able to happen because he saw himself and his father's company as a normal business he was poached into selling to a Lupertazzi competitor which was basically an identical company to Barone Sanitation. Once it was done legally, on paper what could Tony really do? It was a leverage/power move by New York. In all reality in a reverse scenario Tony would have done the same to a New York Lupertazzi ran sanitation company if not for money, for leverage in negotiations with New York.

The Sopranos could get a little careless with the plausibility of some of its story lines. It's hard to believe an owner of a mobbed up waste management company wouldn't let an adult son, who he plans on leaving the company to, in on the business environment they were involved in. Not sure how fast the Lou Gehrig's disease killed Dick Barone, but how shitty of him to leave the biz to his kid without telling him how things worked. Could have gotten him killed.