The second mission is impossible. You cannot build research vessles and the strongest attacking ship you can build is a scout, lol
I feel bad that you feel that way, but in your defense it's not your fault. While the second mission is possible (I went and checked quickly! Try unlocking military drydock and battleships!), you are correct that the campaign does not let you build research vessels. Unlike the other game modes, in campaign after every mission you are awarded 50 research points. I wish that we had better UI/UX to explain that in game, that's my bad :(
Regardless, thanks for playing!