We don't get a POV from Ulthor Young, so we can never know what his thoughts are. Actually he was a planned POV, and I believe I may have written 1 or 2 chapters with him. I definitely planned 2 chapters and wrote 1 but I removed him.
Ulthor Young envies Aeyron Archer. In his mind, Ulthor was supposed to be Aeyron, he was supposed to be King. It was Ulthor's family that had been killed by the Crazed King, and his calling for Ulthor's head which started The Youth Rebellion. Ulthor was the one who went through the hardship and suffering during The Youth Rebellion and he felt he merited something from that, it started with him and should've ended with him. However Ulthor needed support, and he got it through Aeyron Archer and Samuel Royce. However it was Aeyron that became one of the figureheads of the rebellion, with his charming looks and valour on the battlefield. Ulthor just could never be that person.
After the Battle of the Bask, Ulthor sees this as his chance to take the throne for himself, so he rushes to King's Landing with his army despite Aeyron and everyone else disagreeing. They knew Tywon Casterly had his army marching to King's Landing and Ulthor wanted to get there before him. However Tywon made it before Ulthor and was beginning to sack the city, when Ulthor arrived it was too late, Tywon knew to also put blame onto Ulthor so he had sent The Mountain and Hoare Lorch to ask what to do about the queen. Ulthor said to retrieve her but those two dogs had been given a mission by Tywon to murder the queen and her infants. Thus when the children were presented dead, the blame was put onto Ulthor. Why didn't he stop the sack? Why would he murder the Queen? What was meant to be Ulthor's moment in fact was his worst moment, he had been played and shamed. So when Ulthor attempted to crown himself king at the Great Council it was immediately rejected, how could they follow a king that let the capital be sacked. They needed someone that would inspire loyalty and that was Aeyron.
So ever since The Youth Rebellion Ulthor has been envying Aeyron; he lost all his family just to be shunned by those at court that speak behind his back. With the arrival of Joanna at court, here is a person that doesn't judge Ulthor like everyone else is doing, and she doesn't look at him like the others do. She is actually being open to him, and he loves her incredibly for that. Ulthor knows he doesn't have Aeyron's face so he must do something else to woo Joanna, so he tries to spend all her time around her - making jokes with her, trying his hardest to make her love him. But every time he sees Aeyron with her, he feels jealousy. Aeyron took away his chance to be king, he doesn't want him to take Joanna now. That is the key factor that drives Ulthor.
Aeyron has always been antagonising to Ulthor after the war, which has allowed hostility to brew between them. So when Ulthor has the chance to usurp Aeyron he takes that chance with Nestor, because in his mind he can finally right his wrongs with Aeyron. Ulthor's actions in the war are mostly done to spite Aeyron, Nestor is the one who is holding the most of the weight with actual plans with the war - meanwhile Ulthor stays in the east with Joanna. 'Ulthor wants the throne, not Sun’s Champion. It’s only a means to spite the king'. Ulthor just wants to hurt Aeyron and get revenge which is why he wants Nymeria Archer and Larra Archer in his captivity. It's why he also betrays the peace and kills Trystane Archer and his family, because although the Gods will condemn him, it's better knowing that he's caused Aeyron the same pain he felt when his brother died.
The problem with Ulthor is that he presents himself as strong and powerful, which is a total farce. He himself doesn't believe it but he feels he has to portray this image. He only hides his emotion but that doesn't make him a strong man and at points his emotion comes out - 'Ulthor’s eyes caught onto Trystane’s guards and sudden fear was shown in his eyes but he were quick to hide them'.
When Aeyron and Ulthor fight I think we see Ulthor's true personality for the first time. He's afraid of losing Joanna 'Joanna is mine! Always mine.', 'I will not lose her!' - it is the last thing that Ulthor has that he thinks Aeyron will take. Ulthor in the fight comes across as very emotional - I lost everything! When he dies he repeats Joanna's name and the tower, he wants Aeyron to find out - he wants Aeyron to know that he's failed and that he couldn't take Joanna from him.