Sarah Connor in Terminator: The Sarah Connor Chronicles (the Terminator tv show, aka TSCC) went through some changes herself. In TSCC she has calmed down a little but still has a deep relationship with her son. I will talk about her relationships with a few people on the show.
Charley Dixon: This is her fiance that she breaks up with because she feels she has to keep moving on. She also doesn't want him to become involved with the Terminators if they ever show up again. In the show you can tell that they both still love each other deeply but they can't recover from what happened (Sarah leaving him). Charley does end up becoming involved with Sarah's life and is the reason why Derek Reese survived. And, when Sarah decides to leave John because she has cancer, she decides to let Charley take care of him.
John Connor: Sarah Connor is protective of her son and sometimes controlling at times. She is distrustful of Cameron and Riley Dawson because John likes both. One reason Sarah is so close to John is because he's the only person she can really trust. The fact that he saves the world is just another fact about him to her.
Derek Reese: Sarah finds out that Derek is Kyle's brother and probably tries harder to free him because of this fact. She ends up not trusting him because he lied about not killing Andy Goode. I believe she did learn to like him, as she was very heartbroken about his death, but could never admit it. This was probably due to the fact that he wasn't Kyle, just his brother, and that he can be a handful to deal with. The thing that put up a wall between them was that he hid his relationship with Jesse and so endangered John's life (nevermind the fact that John basically knew what was going on and it was his fault, Derek didn't know about Riley knowing Jesse).
Cameron: Sarah Connor was nearly killed by the first Terminator she met and so doesn't trust Terminators. Cameron is no different. Sarah ends up trusting Cameron but isn't even conflicted when the choice comes down to kill her. Why would you care about a heartless machine? Sarah ends up putting up with Cameron for the sole fact that Cameron has been sent to protect Sarah and John.
I'd put in about her relationship to James Ellison (the FBI Agent that at first goes after the Connors but that changes) but he isn't really involved with her enough to warrant it. Maybe with a Season 3 that would've change (as Sarah and James were having to look after Catherine Weaver's daughter).
Also, it seems anyone that Sarah likes ends up dying at some point (Andy Goode and Charley Dixon among them).
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