So, this is just going to be tricky to manage - Bertie got married off only a few years after his sister. The highest the Kaiser ever ranked in the British succession was sixth, right after his birth. I don't think anybody who ranked that low has ever succeeded to the British throne under the Act of Settlement (Victoria was fifth at the time of her birth, and everyone ahead of her was a childless middle aged-to elderly man).
Even if you manage it, I think butterflies are going to destroy this timeline. If the Queen's sons are all sickly, then everyone knows Vicky is likely to inherit, and parliament won't let her marry the Crown Prince of Prussia. She'd be married to some landless younger son who's willing to live in England.
Eligible protestant Princes from royal families around 1855:
1) Prince Albrecht of Prussia, nephew of the King, four years older than Vicky
2) Prince Oscar of Sweden (OTL King Oscar II), younger son of the King, 11 years older than Vicky
3.) Prince Wilhelm of Denmark (OTL King George I of Greece), second son of Prince Christian, 5 years younger than Vicky
There's some possibilities from non-royal houses (a younger brother of the Grand Duke of Baden, notably), but Prince Albrecht actually looks by some margin the best candidate. So likely you don't get a personal union, but you could easily get a Hohenzollern cadet on the throne.