The old core was putting off to much radiation. The new core gives more power than the old, but with none of the radiation. They talked about this in the movie. Maybe not a lot but they did.
They said that Vanko's father worked with Starks father and that both he and his father were Physicists. They also said he was a genius or something at one point. Again very quick, but they did talk about it.
Why did they need to expand on the ideologies? They said that the other family was stealing ideas and selling them. The son and father both were convicted of selling secrets.
They stated at the beginning that Hammer was under US military contract as their arms provider/Maker. With US funds behind him, he has all the means he needs. It was also shown he has the know how to make the suits, but needed some one else to make them work better. Hammer also didn't build drones. He had started making suits. It wasn't until he busted Ivan out of Jail, and Ivan turned the suits into Drones.
I agree it could have had more to it, and it could have had more story but it was what it was. And I found it fun. Was it the best comic movie? Not by a long shot. Was it a fun summer popcorn comic movie, you bet. And I loved every minute of it.