I imagine she had all close to all the techs, but how do you tell a vassal what techs to research?
Once you have a Vassal, you get another Diplomacy option. Click on the name of the Leader (bottom right of the main screen) but instead of trading with the AI, choose the "Let's discuss something else..." option. Follow that one up with the "We would like you to research..." option.
Presumably, if the AI does not have all of the Spaceship techs, then you can get the AI to research techs that don't provide Spaceship Parts as build items.
Also, presumably, your Vassal will not get Spaceship techs in trade, since, hopefully, the other AIs will refuse to make the trade, due to "wanting to win the game..." the same reason that they give to you. Hopefully... I can't say that I know for certain.
Further, you'll want to make sure that your Vassal doesn't build The Internet... keep them away from the Computers tech.
Finally, and the most important part of all, is that you have to remember to actively montior what your Vassal is researching. When they complete a tech, the list of Leaders (in the bottom right area of the main screen) will show a blank value for the tech being researched. At this point in time, the AI has completed the last tech that you asked them to research and now has a bunch of overflow Flasks.
You need to then ask them to research a particular tech, otherwise they'll pick one all on their own and will get a full turn of research plus their overflow Flasks going into that tech--which may even be enough Flasks for them to complete the tech, say, if they had started research on it previously.
So, there is a micromanagement commitment to diverting a Vassal's research along lines that you choose. It's a small commitment, but not one that you want to ignore, or you could be surprised by seeing your Vassal complete their Spaceship before you complete yours or complete whatever other Victory Condition you were going for. Good luck trying to get your own Vassal's capital razed in time to make your Vassal lose!
