Sadly if you look at how historically Kings had treated their wives, George I imprisoning his wife, Caroline has no leg to stand on, no matter how popular she is, no one will want to upset the next in line, George IV.
Plus if you look at how George acted in OTL, I can imagine he will request Parliament to make subsidies for his four children and their two households, being paid into his own purse, keeping the money to live more lavishly.
George III will dote on them along with his wife Queen Charlotte. Although will Prince of Wales want his “insane” father to have much influence. Again I can’t see the way the Prince of Wales changing the way treated his parents ITTL any different to how he did in OTL.
Hopefully after the death of George IV, his children can celebrate the life of their mother and speak her name without feeling like they are walking on egg shells.