Would they? The electoral lines of the houses of Hohenzollern and Wettin retained a relatively close relationship with their ducal/margravial cousins. Although, I suppose that could just be because they would both be in Germany rather than one in Germany and one in a foreign country, so they probably had some of the same interests. More like the relationship between the Palatine and Bavarian electoral lines?
Okay, so Russia can veto Denmark's annexation of Bremen-Verden but not Schleswig-Holstein-Gottorp? However, Russia, post-Nystadt seemed to be interested in closer relations with Sweden, since they married the czar's eldest daughter to the heir of Carl XII. So might Russia support Holstein seizing Bremen instead. Still goes to a cadet line of the Danish royal family, but it doesn't go to either Denmark/Sweden, so there can't be bad blood? Of course, if things in Russia go as OTL and Russia ends up theoretically inheriting Holstein, it could prove an apple of discord.
Um...I think you mean William, Duke of Gloucester. Henry, Duke of Gloucester is Anne's uncle, William's her son.
That said, let's think on this, there are 50+ candidates ahead of Sophia, some of which are pretty insignificant rulers - Salm-Salm, anyone? - any one of them can convert (not saying they will, but they can). Plus, Anne hated George I, Sophia and by extension George II. Georg I slighted her by refusing her hand in marriage, she despised Sophia because she suspected Sophia was behind it - plus Sophia's better health didn't help matters (it was only by a freak accident that Sophia didn't succeed Anne). That said, she also viewed the death of her own children and her deteriorating relationship with William and Mary, as a sort of divine retribution for her betrayal of her dad and brother in 1688. If her daughter, Anne Sophia (the healthiest of her children according to her autopsy) survived, Anne's going to marry her off to George II, both to ensure the Protestant succession and to block George I. (There were rumors, cited by Antonia Fraser in her biography on Louis XIV, that Anne wanted to do this with her half-sister, Louisa Maria, if James III died ahead of schedule). To her mind, as long as her sister breathed, George I/II couldn't claim the throne in their own right.