Few thoughts
If by some miracle (or tragedy) Victoria does end up heiress presumptive and you can get rid of all four of her brothers and their issue i have no doubt Parliament will intervene to amend the succession.
Possibly excluding the descendants of British princesses married to foreign rulers or the heirs to foreign thrones.
Which would exclude both Victoria and Alice and their issue.
Which would settle the succession on the Princess Helena and her English-born and raised children.
Her marriage in 1865 had caused a bit of a family-rift but she remained exceptionally close to her mother and given her strong views on nursing and women's rights would have made rather an interesting Queen considering she survived her mother and would have reigned from 1901 to 1923.
her surviving issue were -
Prince Christian d 1900 in the Boer War unmarried but had he moved up the succession then would undoubtedly have married.
Prince Albert d 1931
Princess Helena Victoria d 1948
Princess Marie Louise d 1956 Married 1891; Prince Aribert of Anhalt; no issue; divorced 1900
Interestingly delaying conception might not have made much difference given the birth dates of V & A's issue: the only ones with a short gap were Victoria and Edward (just under a year), Alice and Alfred (Just over a year) - 1840, 1841, 1843, 1844, 1846, 1848, 1850, 1853, 1857.
If Vicky falls heiress before her marriage then her husband would not have been the heir to the Prussian Throne (Parliament would never have sanctioned it) - if she falls heir later then it again depends on when.
If her children are young and her family agree to dispatch the second son to be educated in Britain (Victoria had reacted with reluctance when her brother in law tried consistantly to try and get her to send Alfred to Coburg for his education) - then parliament might be willing to name her second son Prince Henry as Victoria's heir - passing a bill excluding Vicky and her eldest son (similar to the Coburg succession for example).
If her children are older then I think it is more likely that Parliament will insist on Vicky's and Alice and their offspring being excluded - Victoria's reaction to that would be interesting but at the end it would be a Parliamentary decision.
There was an assasination attempt on Alfred Duke of Edinburgh in the 1860s that you could have succeed to remove him before his marriage.
And at a push you could give Arthur haemophilia like his younger brother Leopold and get rid of them both at some point before their marriages.
Depends when you get rid of the boys and how many of them.
Possible effects:
The Queen was personally unpopular in the 1860s after her widowhood, the monarchy did enjoy a resurge in popularity at times particularly the popularity of the new Princess of Wales (Alix of Denmark).
The height of any republican feeling was in the late 60s early 70s but was mitigated by an assasination attempt on Victoria and the illness of the Prince of Wales (who nearly died from Typhoid fever).
It quickly subsided and the longevity of the Queen helped increase the popularity of the monarchy.
No illness for Edward and things might be different but there was no strong parliamentary support for a republic.
No Edward VII means a less anti-prussian feeling at the British Court in the decade before the First World War (though unlike many in his family George V was less ill-disposed to his cousin the Kaiser), Edward was a major proponent of the Entente Cordiale with France and was very popular in France, though Britain remained a guaranteur of Belgium's integrity of course, no Edward VII also means no Alix of Denmark (whose anti-prussian sentiment like that of her sister Marie of Russia influenced both of their husbands), Edward's distaste for his nephew Wilhelm II was marred by Wilhelm's difficult relationship with his parents and in particular his British mother, given his character his exclusion from the British succession may mar his view of Britain even more.
Few points ref the Coburg Duchy.
Under the family pact - it was decided that in the event of Prince Albert's brother the Duke of Saxe Coburg Gotha dying without a male heir as looked extremely likely - Victoria and Albert's second son would succeed (to avoid the Duchy being ruled by the British King in personal union) - Alfred remained in the British Line of Succession (as his descendents do to this day).
Affie's only son died shortly before his father after a scandal and much pressure was put on Victoria's younger children and grandchildren - who had unlike Affie - not been expected to succeed - the Duke of Connaught and his son were adamant in refusing and in the end it went to Charles Edward the teenaged son of Leopold Duke of Albany.
I think if you exhaust the male descendants of Victoria and Albert - Coburg would have passed (through male primogeniture to the Portugeuse King descended from Prince Ferdinand Georg August of Saxe-Coburg and Gotha and thence to the junior descendants of Ferdinand including the Bulgarian Royal family). So you would also have a succession crisis in the Duchy as well.
Issue: of V and A:
1)
Victoria,Princess Royal, b 1840
surviving issue:
Wilhelm II, German Emperor,
Princess Charlotte m Bernhard III, Duke of Saxe-Meiningen
Prince Henry m Princess Irene of Hesse and by Rhine
Princess Victoria married (1) Prince Adolf of Schaumburg-Lippe; he died 1916; no issue
Princess Sophie married Constantine I, King of the Hellenes; had issue
Princess Margaret married Prince Frederick Charles of Hesse
2) Albert Edward, Prince of Wales, later King Edward VII 1841
surviving issue:
Prince Albert Victor, Duke of Clarence and Avondale d1892
George, Prince of Wales, later King George V m Princess Mary of Teck
Louise, Princess Royal m Alexander Duff, 1st Duke of Fife
Princess Victoria Never married
Princess Maud m Haakon VII of Norway
3) Princess Alice, later Alice, Grand Duchess of Hesse 1843
surviving issue:
Victoria married Prince Louis of Battenberg, later Marquess of Milford Haven
Elisabeth (kd 1918) m. Grand Duke Sergei Alexandrovich of Russia (11 May 1857 - 17 February 1905)
Irene d 1953 married Prince Henry of Prussia
Ernest Grand Duke of Hesse d 1937 married 1) Princess Victoria Melita of Saxe-Coburg and Gotha and had issue, divorced in 1903; married 2 )HH Princess Eleonore of Solms-Hohensolms-Lich (17 September 1871 - 16 November 1937) and had issue.
Victoria Alix kd 1918 m Nicholas II of Russia
4) Prince Alfred, Duke of Saxe-Coburg and Gotha, Duke of Edinburgh; Admiral of the Fleet 1844
surviving issue
Prince Alfred ("Young Affie") d 6 February 1899 Hereditary Prince of Saxe-Coburg and Gotha
Princess Marie ("Missy") d 1938 m King Ferdinand I of Romania (1865-1927); had issue
Princess Victoria Melita d 2 March 1936 married (1) Ernst Ludwig, Grand Duke of Hesse and by Rhine divorced 1901 m 2) Grand Duke Cyril Vladimirovich of Russia; had issue
Princess Alexandra d 16 April 1942 married Prince Ernst of Hohenlohe-Langenburg; had issue
Princess Beatrice d 13 July 1966 married Alfonso, Infante of Spain, 3rd Duke of Galliera; had issue
5) Princess Helena 1846, later Princess Christian of Schleswig-Holstein-Sonderburg-Augustenburg
surviving issue
Prince Christian d 29 October 1900 in the Boer War unmarried but had he moved up the succession then would undoubtedly have married.
Prince Albert d 27 April 1931
Princess Helena Victoria d 13 March 1948
Princess Marie Louise d 8 December 1956 Married 1891; Prince Aribert of Anhalt; no issue; divorced 1900
6) Princess Louise 1848 later Duchess of Argyll
no issue
7) Prince Arthur, Duke of Connaught and Strathearn;
surviving issue
Princess Margaret m Gustaf VI Adolf of Sweden and had issue
Prince Arthur m Princess Alexandra Duchess of Fife and had issue
Princess Victoria (Patricia) m Alexander Ramsey and had issue
8) Prince Leopold, Duke of Albany 1853 (had haemophilia)
surviving issue
Alice d 1981 m Prince Alexander of Teck (Later Earl of Athlone) and had issue
Charles Edward Duke of Saxe Coburg Gotha d1954 married and had issue
9) Princess Beatrice 1857, later Princess Henry of Battenberg
surviving issue
Prince Alexander of Battenberg (later Marquess of Carisbrooke) d 1960 m and had issue
Victoria Eugénie died 1969 m King Alfonso XIII of Spain and had issue
Prince Leopold of Battenberg (later Lord Leopold Mountbatten) d 1922 Suffered from haemophilia no issue
Prince Maurice of Battenberg kd 1914