why do ...

[RasterOps]

Don't be in a hurry. Time heals all wounds... Meaning, relations will improve probably due to killing Doms... or helping the gov by means of quests (probably indirectly)... I'm not exactly sure, but I did have neutral (? blue face) relations with a half dozen planetary govs, but after killing numerous Doms and liberating a system or two, I found the relations had improved to excellent.

You can always payoff government officials. Do this before they go Hostile or the next time you visit (land) you will be imprisoned.

Of course, if a half dozen or more planets are upset then the cost of bribes is impractical. It might be better to go to jail. Unfortunately I have not tested this... yet.