I'm the "senior" engineer in this situation (actually, senior staff -- the other engineer is 'senior', though titles in this company are inflated by ~1 relative to standards at FAANG). I'm the designated engineering leader, and the rest of the team very much likes working with me and respects me a lot -- three of our engineers joined the team citing wanting to to work with me specifically, including one engineer from a previous team of mine, an internal transfer, and an external hire. I think the problem is he simply rejects me as the designated engineering leader, because he recognizes he is more knowledgeable than me about a set of technologies he has more experience with than I do.

I'm glad you brought this up, though: The only other person is the principal engineer, who I do think I have to continue to build a relationship with. That principal engineer worked very closely with the difficult engineer, and the difficult engineer has a lot of trust for the principal. The principal has a lot of trust for me, and supported my promotion to senior staff.

He's certainly resentful he's not running the team. He was told really early on by our previous director wanted him to be the lead of this team, despite big gaps in experience. He made a big deal about "officially" abdicating his role as lead to me when I joined, which was a bit much -- I had no intention of replacing him, but just to get the team functioning and working and not trying to get each other fired. At that point I had been moved against my own will and wanted to keep the door open to me going back to my previous team, which was closer to my interests, in 6-12 months.

I think he was put into a position of too much responsibility too soon, did a very good job on parts of it (the technical parts), and an awful part on other parts of it (the team leadership parts).

I think the direct conversation you mean is one potentially effective way to handle this, but things blew up with the last lead too, who was much more brusque. If I'm not careful, and he sees this as "pulling rank", I can see things blowing up once again.