Elspeth's father has done nothing but worry about her and sing her praises since her first appearance. When he talks about Elspeth not being fit he is referring to the tradition of serving in the army, and he was right. In the past it is shown that she is incapable of following orders and in the present that she struggles to live with the consequences.
Would you expect her father to put Elspeth to shame, in front of someone who he's meeting for the first time?
My own father did make me feel inferior, and my mother was the one who actually criticised me unfairly in front of others. Those two are completely different things, coming from different agendas. My father's approach was about reverse psychology, even though it didn't work. My mother was actually the malicious one, telling everyone how bad of a son I was, in order to look like an angel to them. And guess which one of my parents I hate?
Elspeth wouldn't try hard as she did, to earn her father's approval if he was like my mother. She'd just give up on him and go her merry way.
Yes, everybody knew she wasn't fit for military duty because of who she is, but one had to take the mantle of being the heir after her brother's passing, and Elspeth did it to prove that she was better than him, as well as to keep the tradition.
In the past it is shown that she is incapable of following orders and in the present that she struggles to live with the consequences.
I don't know if you ever part of a military institution but I have. Guess what? Military is made for total morons. And for someone with well above average IQ myself, it was hell to march 5 hours straight, just because some idiots couldn't march properly, or refused to do so. Plus, the command structure isn't that efficient either. Officers are usually stupid, selfish, or just incapable of understanding how to make things work properly. So it's no surprise Elspeth was incapable of following orders, because she actually knew better than those who was ordering her around.
Secondly, I don't think it will be what puts their relationship to the test, but Elspeth's approach
Valentine can deal with Elspeth's approach all day long. He actually reads her very well. Remember their conversation in the pool pub, in Mallorca? He called her out right into her face. I get that Elspeth's overbearing personality can rub some in the wrong way, but Valentine isn't one of those people. I'll go out on a limp and claim that he actually likes that. And he isn't one to fake it until make it.
Remember their conversation, after Valentine helped Elspeth moving and ate dinner? Elspeth asks Valentine if her intelligence really bothers him that much. She'll gain friendship and trust points if he admits her brain scares him. Yet, she'll gain love but lose trust points if he says "not at all". Elspeth values Valentine's honesty more than his love. So she doesn't mind Valentine telling what's in his mind, even if it's not what Elspeth wants to hear.
TLDR: You are way off base with Elspeth.
BTW, I hate Elspeth's physique. She's way too tall, I mean she has to be somewhere around 180 to 190 cm according to STWAs depictions. She has a huge ass and breasts that can put Bessy to shame. But she also has the most beautiful face, with Ines being a close second since they are pretty similar apart from some details. Nothing I say about Elspeth is because of her looks.