Am I reading too much into it or was there something strange about the way that Nick and Diana were looking at each other at the end?

No, I don’t think you were reading too much into it! I’m pretty sure that look was a silent conversation that went something like this:

Diana: Usurper! You are Not My Daddy!

Nick: Oh fuck oh fuck I fucked up I f—

Hopefully someone can explain to Diana about non-nuclear families before she goes nuclear on Nick’s ass.