Erewhon's 'betrayal' of the Manticoran Alliance
I'm not going to go into a lot of detail at this point, but the situation (as Erewhon sees it) is this:
(1) The HR Government backed out of/refused to honor treaty commitments the SKM had made to Erewhon;
(2) The HR government had, unilaterally and without consulting its allies, accepted a ceasefire with the Saint-Just government, and effectively forced the rest of the alliance to go along;
(3) It was clear to their government that the RH was negotiating in good faith to formally end the war and that HR wasn't;
(4) The Pritchard administration was doing its dead level best to demonstrate to the minor powers (including Erewhon) that it was a trustworthy, reformed regime which one again adhered to the principles of the old Republic of Haven which had been seen as the pattern to which all enlightened, responsible governments aspired before the rise of the Legislaturalists;
(5) The HR government had insulted and ignored them in several ways (the reason Elizabeth was sending a personal representative in the first place), rather than consulting with them in the peace negotiations which were supposedly going to end the war to which the Erewhonese had voluntarily made themselves a party;
(6) The HR government and Janacek Admiralty had frozen them (like the Graysons) out of all R&D programs with indecent haste as soon as the active shooting stopped;
(7) The HR government had reneged on a specific pledge by the SKM to help deal with the Congo problem, which posed a significant threat to Erewhon's security;
(8) The HR government had done all of this when Erewhon had withdrawn from its alliance with the Solarian League to join the Manticoran Alliance in the first place because of a combination of the perceived Havenite threat and Manticoran promises that Erewhon would be treated as an equal partner in the alliance and not a poor relative living on the charity of the SKM;
(9) Erewhon's trade through the MWJ, while significant, was nowhere near vital to it. Remember that it, too, has a direct link to the SL and that it is very close the RH, which now has the MWJ closed against it.
(1) and (7) are closely connected, and either, under the Erewhonese honor code would be ample justification for severing any treaty relationship with the SKM. Ditto for (5). (3) and (4) clearly suggested to them that the SKM could not be trusted, and that the reason for that -- not to put too fine a point on it -- was that the SKM's political system was corrupt or decadent enough to permit someone like High Ridge to come to power and stay there despite his obviously dishonorable and (probably) illegal actions. At the same time, it was obvious to anyone who actually looked at the situation in the RH that Pritchard and company truly were committed to reforming their system and correcting the previous abuses, rather than retaining them and using them for partisan or personal advantage. As part of (3), (5), and (7), they did not believe that the SKM could be counted upon to actively assist in their defense in the event that a new war did break out. Further, as members of the Alliance, they had essentially been denied any voice in the final peace terms (as a result of the HR govt's highhandedness and arrogance), whereas by dealing directly with the RH they could end their own state of war with them and do so on terms which they could affect. As far as (6) is concerned, they were eventually being sent home and told that any of the new tech (to which Allied researchers had contributed in greater or lesser degree) was the personal property of the SKM and would not be shared with them. And because of (9), their economy will probably actually improve rather than weaken if they throw in their lot with the RH instead of the SKM.
In addition to all of the above, their own experiences with diplomacy as practiced by the HR government mean that they believe the RH's version of what happened, not HR's version. They know he was a dishonorable, dishonest politician with an inflated opinion of his own cleverness. They have also accepted, in essence, that the Pritchard Administration tells the truth and can be trusted to keep its word. And as I believe was pointed out in several places in WoH, there was no peace treaty between the SKM and the RH. The SKM regards this as a sneak attack in time of peace without declaration of war; the RH regards it as a continuation of an existing state of war because the other side was both not negotiating in good faith and fabricating diplomatic correspondence. Under the circumstances of their own experience with the HR govt, Erewhon has every reason to believe the RH's side of what happened and why.
As far as handing over existing technology to the RH is concerned, I think the Erewhonese have every right to regard what they are doing as a response to being betrayed by someone who already violated solemn treaties it had signed with Erewhon. Under those circumstances, they have no moral responsibility to protect the violator of their treaties from the consequences of its own arrogant, high-handed, dishonest actions by refusing to share weapons technology with their new allies.
In short, this isn't a matter of "betraying" someone for merely "insulting" them. This is a matter of following their own perceived national self-interest in the light of their betrayal by the SKM.