He mistakenly feels he can force the Queen’s hand and plans to marry her to gain access to the vast powerhouse of spells the fairy royals own. The fact she’s gorgeous is a bonus but Manatrix, an old rival, feels Brankaresh would make love to a gargoyle if it helped his career. He's right.
Brankaresh ends up allying himself with the Witch and together they do briefly overthrow the Queen but it all ends in tears - and the Queen is one of those characters determined to ensure they’re not hers. And Eileen? Well it was mutual loathing on sight for Brankaresh and Eileen. Eileen repeatedly warned the Queen about Brankaresh's "smarmy" behaviour. It gave Eileen no pleasure to be proven right when the Queen was briefly overthrown by him. What it did give Eileen was a major headache - leave things alone and Brankaresh gets away with it. Intervene and risk your own life and those of your family, the ones you gave up everything to have in the first place, since Brankaresh and the Witch would not/did not believe in containing vengeance to just the one dimension,