I wouldn't close relations with TRR unless they did something particularly heinous that directly impacted TNP or its interests.
However, after reading the May 04, 2014 installation of The Rejected Realm Times, I would let them make the first move, diplomatically. The easiest way to handle TRR and its new government in term of our relations with TRR, is to approach this with a somewhat Realpolitik coloration - we maintain friendly relations with them, and if they cut off relations with TNP, then it's their 'bad', not ours.
As far as diplomatic dealings with TRR and a government that for all intents and purposes is taking a blustery and belligerent stance with TNP, I would say let them bluster. Unibot is obviously miffed at the R/D neutrality of TNP (just call me Captain Obvious for that statement) but he will get over it. Judging from the content of this little publication (TRR Times), we are all living rent-free in his head, and that's fine. TRR has the government and leader it has chosen. It has been said that people get the government they deserve and that is their choice. If the new found belligerence caused them (not us) to change their relationship with TNP, then that is their loss, not ours.
Frankly, I am not particularly upset by anything Unibot says nor surprised at all.
But back to the crux of the questions.
Cutting off relations with TRR because Unibot ascended to the Delegacy there would not be a good PR move on our part. Such a response from TNP is probably what Unibot is expecting and attempting to elicit. If we cut off relations with TRR for Unibot simply being Delegate there, then we will be made to look reactionary and non-centrist in our foreign policy, and then fall right into the mold Unibot is attempting to cast us in. Now, if TRR cuts off relations with TNP, it makes them, and Unibot look so far off center that their whole region will look like it is falling off the left side of NationStates. Dealing with instances such as this is easy, if TRR and Unibot are going to act rational. If they aren't being rational, then there is no point in dealing with them, at least on their terms. We simply let them act one way or the other and be careful of the image we project by our response or lack of response. In simple terms, we should not be moved to act by anyone's bluster or personal gripes unless forced to do so. If TRR cuts off relations with us, then we simply take the high road and express sincere regrets at such developments and then support whatever diplomatic treatment necessary to deal with them should they terminate relations.