Watty White's idea was not to give a song by Scarlett and Gunnar to Rayna to safe her tour. He actually suggested her to tour with Deacon instead, to perform the old songs they wrote back in the times when they were dating. After singing with her ex at the Bluebird cafe, Rayna comes to realize that she still has some feelings she doesn't want out and that the idea of this duet could cost quite a lot for her personally. We learn that their romance lasted for eleven (!) years, right until the time when Deacon got to a rehab due to his drinking problem. So yes, a lot of painful memories that must bring. However, she doesn't say she doesn't want it, and when asked by Deacon why doesn't she pronounce that their relations and everything is over, she gives a weird speech about how she's trying to do the right thing and she can't. So, she neither wants to be with him, nor does she let him go.
Juliette throughout both episodes kept asking her manager, why Deacon is not on her band. There was very little use in that, because her manager doesn't seem to be particularly skilled, so she keeps screwing Mr. Clayborne (this time him exclusively), until they write and record a song together. But he does say "no" to going on tour with her instead of Rayna. On top of that she has to deal with her addicted mother, who came to Nashville, because she didn't have anywhere else to go. Juliette's manager advises to let mom stay at Juliette's manor, to minimize harm she can cause. In the end of a third episode, Barnes is caught on teenager's phone camera stealing a nail polish, which, I think she did on purpose. I imagine, she'll have to hold a press conference to explain how troubled her life was/is to get to Deacon. Or she's just a kleptomaniac.
The financial adviser of Rayna and Teddy says they're pretty much broke. He suggests to take a loan on the house, which is no longer easy to get, or go on tour with Juliette Barnes, or borrow money from Lamar, Rayna's father. Lamar sends a loan offer of 500 000$, but he puts some clauses to the loan agreement that restrict Rayna's touring possibilities. When he appears at the school talent show to watch his granddaughters perform Juliette's song (this time their mother didn't seem to mind the low quality of this song), Rayna tells him to leave very rudely. She later learns from her sister that Lamar's attitude towards her career could have been caused by her mother's affair with some songwriter. Rayna comes to her dad with good intentions, but as she hears that he believes her to disregard her family like her mother used to (which is completely true), she insults him again, blaming him for her mother's affair.
Watty offers Gunnar and Scarlett to record some demos for them. Scarlett worries that her boyfriend Avery would be jealous, and he is, but he tells her to do it anyway. Then at the studio she screws up to the point where Watty offers to give the song to some other girl. Once again, Avery helps Scarlett overcome her insecurities and comes to support her in the studio. Because he's outlined as "bad" person, his secret motive could have been being introduced to Mr.White.
Teddy probably did some illegal stuff in the past, something that will obviously hunt him down in his campaign.
So, to outline characters' traits: Rayna is a hypocrite, Juliette - sophisticated and evil, Deacon messed up, Scarlett - silly/naive, Gunnar - plain idiot, Avery - layered, Teddy - weak and cowardly, Lamar - excessively controlling.
S01E02: 5/10S01E03: 7/10