Britain was so unrepentantly racist that Victoria had an Indian god-daughter? Victor Duleep Singh married an English noblewoman, with the intervention of the royal family, so it's not an insurmountable hurdle. The main problem is that a marriage to an Indian princess would yield no diplomatic fruits, and these weren't the days when royals married for love.
True, but Prince Victor Duleep Singh (b. 1866) and Lady Anne Coventry never had children. According to Anita Anand's biography of Victor's sister, Sophia Duleep Singh, Queen Victoria told the couple they could not be allowed to have children.
I think it might work more effectively to have Victor (or his younger brother Freddie or have the youngest brother Eddie recover from the illness that killed him) fall in love with one of King Edward VII's daughters, Louise, Princess Royal (b. 1867) or Victoria (b. 1868), probably Maud, later Queen of Norway, (b. 1869) is not such a good choice unless you're trying for the maximum number of butterflies, or Princess Alice's daughter, Princess Irene of Hesse and by Rhine (b. 1866), or Prince Alfred's daughter, Princess Alexandra of Saxe-Coburg and Gotha (b. 1878), or Princess Helena's daughters, Princess Helena Victoria of Schleswig-Holstein (b. 1870) or Princess Marie Louise of Schleswig-Holstein (b. 1872).
But again, whether the couple will be allowed to have biracial children, especially while Queen Victoria is alive seems unlikely.