I think your projecting the world o 1914 unto 1898.
Switcheroo much?
In 1898, France and Britain were the traditional allies of the US, Britain the traditional enemy. I doubt if either France or Russia is going to intervene to fight the British and anyone who helps them for the Americans. They would be quite happy to let them all bang themselves up. The Kaiser would as well. The Germans have greivences galore against the British
Not really Germany or at least Wilhelm wanted to acquire a colonial interest in Venezuela but were blocked by the Monroe Doctrine. Germany (including Wilhelm) would quite like a British alliance as it came with all kinds of juicy advantages. France and Russia (I assume that is who you met by your first Britain?) were quite often neither here no there in regards the US as mostly it did not impact their strategic picture and vice versa.
Nor can you say that the kaiser is openly hostile to America. He's interested in preserving the Hapsburg monarchy in Spain doesn't mean he's going to go invade anyone. what do the Americans have that he wants? Let alone something that he would go to war over. The British have Canada and Caribbean Islands, British Honduras and Guyana. What is Germany going to get by war with the Americans?
Well yes I can, in fact he had some quite choice words to say about America however it is true this negative attitude only becomes apparent when the US truly stats throwing its weight around in 1898. He had been somewhat hopeful of expanding German influence in the Spanish Empire which it is worth noting had been under Bourbon Monarchs since Philip V.
Nor do I posit German intervention in a war in the Americas. I am sort of baffled why the British would fight, for it is likely to be them doing almost all the fighting and jeopardise considerable trade interests in the US, for Spain to hold on to colonies it is in the process of losing nor for the US to risk facing the British who are far and away more formidable a challenge on land and sea and in terms of industry and finance than Spain. The other European powers would likely look on and watch.
However Germany seeks to expand its Empire unlike the fairly content French and the Russians who are interested in their near abroad and thus more of headache for the British. Thus Wilhelm can dangle his Americanophobia before the British allowing the British to safely tame one of the only two naval powers who can potentially catch them in the long run, the other being the US. If a European War breaks out then the US is fairly likely to not intervene and the British are not likely to be doing that much on the Continent themselves. However the gain for Germany of not being blockaded is obvious even if the British can not be induced to join in and hit the French in their Empire and on the high seas.
If the British have been banged up by an American war they would be even more inclined to seek peace with the Franco-Russian alliance which threatened their Empire everywhere. With their finances wrecked by the war with the Americans and the Boers, the British aren't going t o be in a very adventurist mood. Are the British going to sign the Japanese alliance and risk war with Russia, France and the Americans?
The British worse case scenario is a successful land invasion of Canada, this still leaves an intact RN to outface France and Russia, this would be the case even without an allied Germany but doubly so with one.
ANd what if the Russians just take advantage of British preoccupation to eliminate the Japanese threat?
The British did not ally with Japan until 1902. The Russians might in this TL avoid conflict with the Japanese if Germany is chummier with the British as Nicholas II might twig that Wilhelm was BSing about coming in on his side against the Yellow Peril.
To be frank, I see no reason anyone would stick their necks out for the British and plenty of reasons to sit back and let the Americans and British bang the hell out of each other.
Now if WWI happens OTL then the Kaiser would be a big winner no one denied that. But is it going to resemble anything like Otl? Doubtful
The thing is you argued for an exact reprise of OTL WWI but with the US not trading with the British as per OTL. I am not asking for anyone to stick their head out for the Brits, I am a bit baffled that the Brits might stick their fingers out for the Spaniards, however Kaiser Bill merely is posited as acting in his own selfish interest to Germany's gain. The difference is my scenario potentially follows from the POD while I struggle to see how yours even relates to it.