If Wilhelm wants to have good relations with Britain, he'd better learn to let Britain call the shots for German policy.
Britain was running roughshod over German interests in the Transvaal, and threatening war and blockade if Germany resisted, before Germany built the HSF. Because Britain didn't want yet another strong nation intruding to insinuate her own interests (France had already learned her lesson at Fashoda) -- even if those interests were entirely legitimate according to the standards of the time.
It will help in this regard if you recognize that Britain was very much the hegemon in overseas affairs, and she knew and liked it.
Plus, unified Germany arose too late, in a Europe just "big enough for four". If she makes any waves, colonial or Continentally, Britain will side with the Long-Established Powers. Especially Russia, which can cause serious trouble for Britain around Persia and India, but also France with whom Britain had, at long last, worked out a satisfactory (to Britain, at least) modus vivendi. Germany was the unwelcome parvenu; sorry, Bill, tough luck old fellow.
I'd recommend you read The Sleepwalkers, by Clark.
Bottom line, no matter how Anglophile Wilhelm might be personally, it won't gain him anything unless he Knows His Place.
And that's going to be a real problem for the Kaiser we all know and love...