I LOVE Imhrahil, he’s my favorite bit character; intelligent, responsible, actually thinks about things!
He so does not have daddy issues (at least, in my conception of him). In fact I envision him as having a loving daddy who made a point, when Imrahil was young, of taking him along when he was doing ruler-type things and showing him how everything worked. Young Imrahil would sometimes ask stupid questions, but his dad would never laugh at him, and patiently explain why the decision was made that way. Occasionally, especially as Imrahil got a little older, he’d (mostly accidentally) hit on a point his dad hadn’t thought of, and his dad would praise him for coming up with good advice. Also, Dad always stressed that they, the rulers, were responsible to the people, and not the other way around.
He idolized his dad so much that maybe he shortchanged his mom a little, though she loved him just as much. She was mostly a typical stay-at-home mom, although even after she married and had kids she continued some of the physics and astronomy experimentation she had done as a teenager (in fact, that’s how his parents met; she was at the top of a tall tower dropping balls of various sizes and weights, trying to see which fell first, and he happened to be walking by. First she had to yell at him to make sure he didn’t get hit by a ball, and then she enlisted his help in seeing which dropped first). He probably absorbed a great deal of her hard-headed rationality, but was more dismissive of her talents than he ought to have been.
He wasn’t particularly jealous of Aragorn as King, as that was a little more responsibility than he would’ve wanted, but one must admit that he did wonder a little what it was like to ahem be married to an Elven woman.
He thought Eowyn was good-looking but a bit on the brainless side, and was frankly a little astonished that Faramir, whom he greatly admired, thought she was all that. He teased Faramir about his infatuation quite a bit, which Faramir was a good sport about, and when Imrahil fell head-over-heels for Faramir’s cousin [um, did he have cousins? I don’t have the books with me] Faramir didn’t even say anything, just smirked at him.