Well, Clint knew that that was a Widow trying to kill him. I assumed he knew who that was once her mask came off. Yelena has no idea what happened with Nat's death, just that Clint was there. She's operating off of Julia Louis-Dreyfus's order from the post-credit scene from Black Widow.
I agree, I think they will eventually talk it out and join up. I mean, Marvel has made it pretty clear that Yelena will assume the Black Widow role. Of course, I guess she could become a baddy, but I don't see that. Well, not really sure what JLD's game is since she is recruiting people.