You don't control the Crusader in the second mission.

Generally, you want to preserve your starting capitals and fill out your fleets with fodder. This should keep you alive long enough to move down the tech tree and put together fleets that are competitive with the Drengin.

Fleet composition isn't as important here as tech, but in general you want high-firepower "capitals" and high-durability "escorts". Carriers are also very strong in all roles (the fighters are classed as "escorts", but have tons of firepower as well) and putting together a big blob of carriers should be adequate if you're not feeling inventive.

if you want an easy victory, build lots of carriers. those things are overpowered. if you want a fair game, destroy their forward starbases so your planets are out of range of their fleets, and tech up until you have enough firepower to kill their fleets with conventional ships. 

you may not even have to tech up that much. IIRC there's quite a lot of resources on that map, so instead of researching higher tier weapons, you can grab all the resources, get some mining techs to get more out of your mines and put together a fleet with lots of the "prototype" weapons that are avaiable very early, require resources and have the firepower of endgame weapons. if you can put together one fleet that can kill their patrol fleet without significant losses, you can probably go on the offense since their garrison fleets are about the same level of power.