The Abyssinian crisis was a blow to the good work of the League of Nations. Abyssinia, an Independent member of the League was taken over by Italy (a council member), and although the League tried to take action against Italy, the economic sanctions that were imposed on it were ineffective. Britain and France were also unable to prevent the conflict and it was clear (through the Hoare–Laval Pact) that they were more interested in having Mussolini as an ally against Hitler. This damaged the reputation of the League and led to its rapid demise. However, Mussolini was annoyed by the sanctions and increasingly looked at Hitler for support. In fact, in 1936, the two leaders developed closer relations with the Rome-Berlin Axis Pact and agreed to work more closely together. Most importantly, it proved to Hitler (and many other people of the time) that the League and the method of collective security would not work and so the League was not at all significant the attempts to deal with Hitler.
The collapse of the League of Nations led Hitler to follow a more aggressive foreign policy for Germany. One manifestation of this was the Remilitarization of the Rhineland in March 1936. Although it was a direct breach of the treaty of Versailles, Britain and France did not react. Hitler had used force and was allowed to get away with it. This proved to Hitler that the appeasement sentiments in Britain and the threat of war could be used to achieve his demands. But above all, the remilitarization also made it difficult for France to put pressure on Germany in the future and therefore Germany was in an even stronger position against any attack from the west. This made it easier for Hitler to now focus on the East and achieve his early foreign policy.
The Spanish Civil War had a limited effect to the peace in Europe in the late 30s. It was seen as a war against Fascism, the ideas of both Mussolini and Hitler, between the Republicans and Nationalists. Although it was the first serious conflict in Europe since WWI and weapons of mass destruction were used for the first time, the British and French policy of Non-Intervention partly succeeded in that the war was contained in Spain. The devastation caused by the war created a widespread concern about modern warfare, particularly to the damage caused by air raids. In fact many people at the were pushing politicians to prevent another war.
From the above evidence, it is clear to note that all three events undermined the peace and stability of the area but each one had a different impact. As stated before, I think the Remilitarization of the Rhineland did the most to undermine peace. As Britain and France did not respond to it, Hitler gained even more confidence to pursue his early foreign policy: to unite all German speaking people and to provide more living space (Lebensraum) for all Germans. This strategic move allowed Hitler open the gateway to conquer more land in Eastern Europe to accomplish his goals (as he did in Austria, Czechoslovakia and Poland). These events led to the complete collapse of peace and the outbreak of the Second World War.