My pet US CP is thus
Early 1890's the Silver-Gold split in the Republican party is more acrimonious, to the point that when Senator Teller switches parties, the Republican leadership is vindictive enough to kill anything he originates on general principles
Fast forward to the Spanish American War, have the Spanish do enough better to get the US pissed off, but not enough better to win or allow European Intervention. As a result the US takes the entire Marianas and Caroline Islands in the Peace Treaty, and absent the Teller amendment the status of Cuba is left in limbo for a few years. In addition with a worse performance the US feels the need to enlarge its military to a rather greater degree than OTL
US control of extra bases in the Pacific, possible full control over Cuba, and greater expansion leads to some tension with the UK, who look with a bit of worry. Because of this the UK does not send the same indications as OTL before the Venezuela Blockade, leading to worsening relations and the US not agreeing to arbitration in the Alaska boundary dispute
That dispute continues to simmer on, preventing any real rapprochement. TR eventually ends up settling Cuba's legal limbo by annexing it, angering Britain, and leading to an insurrection there that some in the US accuse Britain of supporting
Other events lead to the two nations being less than friendly. Also, somehow, the few US Germany disputes over islands get resolved easily, peacefully and to everyone's satisfaction. Due to butterflies the Taft-TR split gets healed and TR is elected in 1914. When war does break out in 1914, probably over something other than the Archduke, the US protests more over the blockade and US ships get hassled more. At the same time Germany has the U-Boats be more cautious RE US shipping. The US still sells to the Entente of course
Anyway as the blockade continues to annoy the US and there is no Lusitania type incident. TR uses the distraction of the war to send troops to the disputed areas and solidify US control. This results in incidents with Canada, and TR does not back down, figuring the UK does not want the US joining in, things keep escalating, but stay short of war, until incidents at the blockade line get egregious enough for the US to declare war