If I were to design something like this, here's how I'd implement it. Note that i have no clue how planets are defined in the game. I also think in the context of a human, and I don't know how the AI could respond.
Anyway, here's my $.03 cents.
Such a massive ship needs a massive hull. Introduce "Titan" level hulls. This means more technology to research, which would take a lot of time.
A Titan ship is in effect a mobile space station. Introduce a "Mobility module". This makes Space Stations more tactical, since you need to balance slots with sheer numbers for something with very little defense itself. This particular upgrade would be high on the tech tree, since you need to also have 'Enhanced Structural Integrity' (A new upgrade which is also needed for Titan hulls).
Titan ships also have the more practical problem of actually flying. A constructor is often enough for building a basic space station, but Titan Hulls need more - One constructor can't handle the volume of work needed for such an undertaking, so now you need to build Ship Construction Yards, which are a new kind of Space Station.
We now need a weapon... A Phase Matter Distorter! In order to build the Phase Matter Distorter, you need even more technology; particularly of Phasers and Mass Driver tech. This would be a combination of the pair.
So now you have a mobile space station which can mount shuttle weapons. It can act as a short range influence star base (it's INCREDIBLY intimidating).
So now that you have a game breaker, how does it interact with the environment?
DESTROYING PLANETS
Before I go on, I think it's important to note that the power of the ship is not the hull class, but the size of it's weapons and defenses. In effect, it could have a relatively low HP rating (it's big, but it's also an easy target). It can also mount a lot of defense, which must also be balanced with it's weaponry. If you want to mount a Phase Matter Distorter, you'd sacrifice a lot of space in the process.
Moving right along, each planet now has a hidden 'size' value which is based on it's class. This value is how much energy is required to destroy it. A typically habitable planet has a class value of between 6 and 11, so they would need a charge of 6-11; in order to aim for the most critical part of the planet, you need to do some heavy scanning and calibrating and planets which are particularly dense are harder to pinpoint. Adding to the difficulty is the existing infrastructure on the planet, adding interference to the scanning (charging) process.
Warnings would come to the players via GNN, and could be formatted as "Citizens shudder! The Terrorstar will be in target range in X weeks/turns!" In effect, this makes the Terror Star itself a bargaining chip, since other players can see the plight of the planet.
Using the Terror Star would increase your 'evil' rating, and may also demoralize planets with a low influence, who may then defect to other civilizations. Each use would permanently reduce your civilization's influence and could possibly send it into the negatives (the more you tighten your grip, the more star systems slip through your fingers!).
If you wanted to be lazy, you could have the Terror Star counted as an Influence, military, and economy star base, and have that multiplied by 2 to freak out the AI. I have no idea how the Computer would deal with them...
This post is already much longer than I'd originally intended, but I thought I should toss in a few details, personal ideas, and some new game mechanics to balance out my weakly veiled Star Wars references. I wish I could be more helpful...