Ice and Fire from Afar

A mischievous god was summoned to the world of Ice and Fire, attempting to control it, but was defeated. After losing his memories and powers, he tried again, but somehow ended up going astray in a heartwarming (?) story. Note 1: Before chapter 29, the protagonist doesn't even realize he's a mischievous god; he's just a babysitter with a dragon. If you don't want to read silly stories about children, you can start from chapter 29. Don't overthink it; treat it like children's literature. Note 2: The protagonist's apparent identity is Rhaegar's only son; his two older children are gone. His body (the vessel) grows extremely slowly (he looks like a child), so his marriage to Cersei is a political alliance; they are husband and wife in name only, but the protagonist is actually childless.