I suspect its some kind of bug right? I had no crashes or warnings while loading the mission.
Sounds like the game isn't reading the correct files. Make sure you specify the MOD directory in the launcher. -mod DarkChildren . Though, if you did as the first post says and just dropped the VP into the main directory that's cool. Make sure you've not got any other VPs in that directory, and make sure you don't have any tables in your data/tables/ directory either (ie C:\TheBabylonProject\data\tables\) as these will overwrite the VP.
The reason you're in a Ulysses is because that's the first fighter in the ships.tbl and is therefore the default when the appropriate ship cannot be found.
Note that this mission/campaign also needs The Babylon Project. It's not a simple FS2 mod.
So in summary:
1. Make sure you're using The Babylon Project. Not Freespace2Open, not WingCommanderSaga, etcetera. .. .
2. Make sure that the VP is in the main directory, or alternatively, in its own directory and that the launcher points to that directory (ie -mod darkchildren for c:\thebabylonproject\darkchildren\ )
3. Make sure that there are no other VP files in the main directory, aside from what is required by the Babylon Project. (ie other 3rd party campaigns).
4. Make sure that there are no tables from other mods in the data/tables directory.
Should work after you do that.