I can't really do justice to this question as it is kind of broad but, this was balance of power politics at its finest. Britain essentially was able to contain france on the sea and its commercial success allowed it to have financial influence. All of these 'coalitions' had Britain as a key backer. On the land side of the continent anyone that wasn't france had an existential interest in joining Britain against France. They just kept trying until Napolean screwed himself in Russia.