Faced with a Russian expansionist policy and in reaction to the various coups led by the Putin presidency, the member states of the EEU decided very early on to set up barriers (as much as possible) to Russian hegemony.
We can think first of the fact that during the negotiations on the future terms of the Astana Treaty, Belarus and Kazakhstan insisted on the need to have an almost systematic recourse to unanimity. It is a remedy that has already proven itself in world history. One can think in particular, by way of illustration, of the famous compromise of the American federalists when they agreed to create an upper house (Senate of the United States) so that the rights of the smallest States are not crushed by the large ones (as Virginia could have done with Rhode Island for example). Weak states often require recourse to intergovernmental representation or unanimity voting to guard against the power of large countries. This is the case in the EEU. Thus recourse to unanimity obliges the EEU to make only a minimum of commitments. If this prevents a stronger integration, like that of Europe, it nevertheless allows the states of the UEE to bend Russian domination in the decision-making process.
Then, Kazakhstan acted as a real counterweight to Russia in its foreign policy. For example, it was Kazakhstan that insisted that the word "Economic" appears clearly in the title of the international organization (Russia wanted the shorter name of “Eurasian Union”, a term still used in the Russian media by the way). Similarly, Kazakhstan has led the resistance against Russia on issues of citizenship of the Union or the creation of a common currency (which would have resulted in the economies of member states being swallowed up in the Russian financial system). Kazakhstan also opposed Armenia's entry into the organization, preferring a Turkish candidacy. Although in the end the Russian position prevailed, Kazakhstan showed that there was another power at the gates of the ensemble that could compete with Russia.
But the strongest challenge launched by Kazakhstan and Belarus to Russia was their non-recognition of Abkhaz, Ossetian and Crimean independence. Thus, Russia found itself without support in its foreign policy. At the same time, Kazakhstan maintains a multi-vector foreign policy as it equally courts the EU, the United States, China and Turkey. In the end, Kazakhstan bows to the will of the Kremlin only because of the geographical proximity and because of the weight of the Russian population in the north of the country (Putin often playing the threat of a desire for the Russians to join the near abroad to put pressure on its neighbours).
The most bitter failure for Russia remains Ukraine's non-adherence to the Eurasian project. Indeed, Ukraine is not only a significant economic and industrial power, it embodies the real bridge between Russia and Europe. Thus without Ukraine, the Eurasian project is struggling to take off. Putin pressured former President Yanukovych in 2013 to stop negotiations with the EU in order to favour an EEU membership. We know what happened after.
Russia, having carried out aggressive operations against Ukraine, not only managed to lose all hope of rapprochement with this country, it also sent the wrong signal to the other member states of the EEU. It is hard now to imagine the EEU evolving favorably for Union-level integration with such great mistrust on the part of the former Soviet republics in view of the imperialist behavior of their big neighbor Russia. By way of illustration, it is enough to see that Armenia joined the EEU only under Russian pressure and might not have done it otherwise.
Russia maintains this ambiguous role of engine of integration while being its main obstacle due to its authoritarian behavior. If before it was possible to criticize a CPSU opposed to the national idea, now it is nationalist Russia which seems to want to impose by force an integration which first benefits its geopolitical interests. Which brings us to the last axis of reflection on Eurasian integration: the absence of a “Union of law”.