I think we can tell Radahn loved his family and was loved by them, even if theres very little to no verbal confirmation of this in game.
We have the presence of the large Stargazing Altar in Redmane Keep to begin with, proof that he still watches the stars like his mother probably taught him too when he was young.
We have his portrait present in Volcano Manor, showing that he must have had a good relationship with his elder brother Rykard, as not even Ranni has a portrait in his home, and those two conspired with each other!
We have Abductor Virgins present across Caelid and in Redmane Castle specifically, showing Rykard willingly gifted them to his brother’s forces (similarly to him having them placed at Raya Lucaria to guard their mother from intruders.)
We have his innate talent, and training, with magic that he utilises in combat. The likelihood that an Alabaster Lord was arranged as a tutor for him by his family being high considering its location near Caria Manor in an Evergaol. Showing they wished to support him in his pursuits.
We have his pride in his Red Hair, which yes does come from his pride of being a Son of Radagon, but I would argue it also shows his pride in Ranni and Rykard as they too possess the red hair of their dad.
Even though he was effectively sent away to Sellia to learn gravity sorcery when he was younger, it’s likely that this came about either as a result of the Alabaster Lord being unreliable, or out of Rennala seeking a better place for him to learn gravity magic for his aspiration of easing the burden on his favoured mount.
He confronted the stars alone, an act of heroism and he crushed them. The why of this is unclear, but some believe he may have done it to protect Ranni from a dark path, that the Snowy Crone was leading her down.
There may be a few other instances to make note of, but I don’t believe he ever disliked or hated being a Carian. As much as he aspired to the Heroics of Godfrey and Radagon, and may have stalled Ranni’s fate. Though admittedly this may have been accidental, since during the Starscourge Conflict he was seemingly protecting Sellia from a starfall event.
