Character Analysis
To put it simply, Baxter has pretty much no role in this book until the final hundred pages. Baxter isn't a bright guy, and his bad temper has lost him his wife, his job, his friends, and his health. (There's kind of a thing with men and anger in Sons and Lovers.)
Baxter is actually a lot like Walter Morel, if you think about it. The main difference is that Baxter seems redeemable. And Paul seems to buy into this notion that Baxter can end up a good guy after all.
At first, Baxter hates Paul (and pretty much everyone else) for his smugness: "Finding the lad's impersonal, deliberate gaze of an artist on his face, he got into a fury" (8.124). See, Baxter's "whole manner [is] of cowed defiance, as if he were ready to knock anybody down who disapproved of him" (8.124). He doesn't like it when anyone acts superior to him, but especially some artsy little twerp like Paul.
You can imagine how Baxter feels when he finds out that his estranged wife is dating Paul. He kind of loses it, and then his life starts falling apart. He gets kicked out of his favorite bar, his friends turn on him, and he loses his job at Jordan's Manufacturing.
So, Baxter's not a clever man. And he's not all that strong-willed. But there is something in him that Paul likes:
Paul and he were confirmed enemies, and yet there was between them that peculiar feeling of intimacy, as if they were secretly near to each other. (13.2)
Think arch-nemeses in classic comic books.
It is also possible that Paul likes Baxter because he feels he can redeem Baxter, in a way that he could never do with his father, Walter. Maybe by saving Baxter, Paul can give Clara the husband that his own mother (Mrs. Morel) never found in Walter. Or something. It's all very complex and incestual.
Anyway, it's only when Baxter is completely broken down into nothing, "driven to the extremity of life," that he is willing to "crawl back [to Clara], and like a beggar take what's offered" (14.510). In this sense, Baxter becomes a source of healing in the book. Unlike Walter Morel—or even Paul—Baxter is the only man in this book who learns his lesson after hitting rock bottom.
In this sense, he's one of the book's most hopeful characters. Which is depressing. Because he's not someone we'd really like to stake our hopes on.
Baxter Dawes's Timeline