Love the idea here's a few thoughts
Assuming Frederick and his wife have children - then no marriage for George IV in the short term - if Frederick has issue Parliament is less likely to offer financial incentives to George to "do his duty".
Once he becomes Regent then George will exercise influence over his nephew and niece and their marriage choices - given the Duchess of York was close to her family I would suspect she will be keen for a Prussian marriage for one or both her children - her half nephews are the right age and in the post Congress world might have been a suitable match for her daughter.
I think Anna Pavlovna is a likely match for the Duke of York's son - The Prince Regent will definitely encourage the alliance - and a British match at this period for Russia is not as complex as it would be in a few decades - Anna's marriage to the Dutch Prince of Orange was part to mark Russia's alliance with the West.
On Anna Pavlovna she might be a bit happier with a slightly more formal court than the Dutch one - she was very aware of her rank and position compared to that of her husband. If i recall the deal was her children would be raised as Protestants but she remained Russian Orthodox - so suspect that would also be the case assuming the Prince George of York (I think that's more likely than Edward given George III will be the final decision maker on the name and its his first male line grandson) is not too distasteful to her.
Prince Frederick, Duke of York and Albany (16 August 1763-5 January 1827) M. 1791, Princess Frederica Charlotte of Prussia (7 May 1767 - 6 August 1820)
Issue:
Prince George Edward of York and Albany, Earl of Ulster (b1793-1854) M 1816 Grand Duchess Anna Pavlovna of Russia (18 January 1795 - 1 March 1865)
Earl of Ulster from birth, Duke of York and Albany 1827 King of Great Britain as George V in 1830
and had issue:
1) George Frederick b 1818 (Prince George of Ulster 1818 to 1827, Earl of Ulster 1827 to 30, Prince of Wales etc from 1830)
2) Charlotte Amalia b1820 created Princess Royal 1830
3) Alexander Edward b1824 created Duke of York 1835 later Alexander I of Hanover.
4) William Paul b1825 created Duke of Clarence 1835
5) Sophia Mary b 1828
Letters Patent issued by George Prince Regent on January 9th 1818 - All children born to Their Royal Highnesses the Earl of Countess of Ulster were to bear the style of Royal Highness and Prince or Princess of Great Britain and Ireland - had he not issued the patent the children would have remained His or Her Highness as the male line great grandchildren of a sovereign until their father's accession.
During the revolutions of 1848 the King was forced to defend his rule in Hanover and the limited constitution imposed by his late Uncle George IV - he imposed a new constitution in 1849 which satisfied most and indicated a plan to enable his second son to succeed in Hanover (the Prince of Wales having frequently referred to the German state in uncomplimentary terms) - The Duke of York was promptly proclaimed as Regent of Hanover in 1850 and succeeded his father as Alexander I of Hanover in 1854 - there was strong support for this agreement from Prussia and the same year Alexander was betrothed to the 16-year-old Louise of Prussia.
Princess Charlotte Frederica of York and Albany b1795 m 1816 William Frederick George Louis of Orange-Nassau later William II of The Netherlands ( 6 December 1792 - 17 March 1849)
Had issue
1) Wilhelmina Frederica of Orange-Nassau b1819
2) William Frederick George of Orange-Nassau, Prince of Orange b1823
3) William Henry of Orange-Nassau b1826
The Duchess of York and Albany had high hopes for her daughter to marry her half nephew Frederick William of Prussia or his brother William but her hopes were frustrated when her brother in law preferred instead the Prince of Orange and in 1816 the Princess was formally betrothed to William of Orange.