I don't see what the big offense is here. I agree with your description but I don't see how any of that makes Kennedy hate-worthy.
It's Buffy's house, Kennedy is a guest there. It's basic human decency to not look down your nose at the person who is basically providing you with a safe roof over your head so you don't get murdered by bringers.
Also a bed is a personal space. You share it with someone you trust and feel connected to romantically or platonically (and who won't murder you in your sleep), otherwise you sleep alone. Even more so than that, Tillow shared a bed, meaning that one side was Tara's. As we see from TKIM, Willow isn't ready to move on, so essentially Kennedy is inviting herself to sleep in Tara's spot.
So Kennedy blows off the desert training because she thinks it's pointless. Buffy went because she was interested in what the desert could tell her not because she was ordered to. Kennedy wasn't interested and so didn't go. Still Kennedy very much wants to be a slayer and she comes through when she's most needed. More than the other potentials that went to the desert.
Giles didn't take the potentials to the desert for the fun of it, it was part of the potential's training; and as a potential, Kennedy should've gone. It's an example of how she thinks herself above the other potentials, even though they're all in the same boat aka hiding out at Buffy's for protection.
If Kennedy wants to be a team player, she needs to start playing as part of a team, not cherry picking what she does and doesn't want to do. Likewise during the training yard, Kennedy should've been training with the rest of the potentials, not barking orders at them.
She's entitled to that opinion and to tell Willow that opinion. It's not like Willow is offended and Kennedy goes on and on about it because she doesn't and Willow isn't bothered about it.
Consider the difference between:
"I'm not into the whole magic scene but it's cool that you are"
and
"I think magic is a bunch of fairy tale crap (even though it's played an important part in your life) but you can like it if you want"
You can think something is rubbish but don't call it "crap" to somebody's face when it's been an important part of their life. If Willow had never gotten involved in magic, she never would've met Tara. Also learning magic improved Willow's confidence, it means something to her. Essentially what Kennedy has done is made clear that she thinks magic is a load of crap but Willow can continue engaging with it if she wants even though magic is still a load of crap.
I think that it was unhealthy for Willow to see kissing a new person as an insult to Tara so I'm okay with that being worked through with Kennedy.
You know who sees romantic interaction with a new person as a betrayal towards their deceased partner? People who aren't yet ready to move on from their dead lover.
Moving on takes time and it's an emotional state of feeling ready to begin a new romantic relationship without seeing it as a betrayal to the dead partner. Willow was not at that stage yet Kennedy didn't care. Moving on is important, and some people struggle, but it is something that can't and shouldn't be forced.
A common "defence" of Kennedy that I often see is that she "forced" Willow to move on because otherwise Willow wouldn't do it. Grieving doesn't have a time limit, it takes as long as it takes. Fred would be more in line with the kind of person Willow is attracted to (eg similar personality to Oz and Tara) and you would be able to see Willow feeling guilt that she's developing feelings for another person. However, I doubt Willow would be begging forgiveness from Tara, because Fred isn't pushy like Kennedy. Fred and Willow would bond, you've got the whole science vs magic angle, Willow would feel attraction to Fred and confide in Xander about what it could mean, but because Fred isn't the type to push for a romantic relationship when Willow isn't ready, there would be no kiss (at least not until the very end of the season as a display to show that Willow is finally ready to move on.).
In the episode where Willow crosses over to Angel, she and Fred bond and Willow was obviously feeling some sort of romantic connection because she felt the need to inform Fred she had a girlfriend (ergo they couldn't develop their flirtation further). Whether or not Fred felt the same is slightly irrelevant as the point is that Willow felt a romantic attraction towards Fred. There is absolutely no reason why Willow would go for Kennedy and if I remember correctly, Willow actually cheats on her with a snake demon lady and ends their relationship.
Kennedy didn't avoid the final battle that wouldn't make any sense considering in every other battle she's thrown herself in front of the others and fought. Let's not forget how she was asking to go and back Buffy up in her fight with the ubervamp. But no apparently she has a personal problem with Buffy.
Kennedy was sat with Willow far away from the fighting, she was nowhere near the Hellmouth hole. Like I said, it would've been better if Xander and Kennedy had switched places so that Xander stayed with Willow whilst Kennedy guarded the hole ready to take out any escaped ubervamps. As it is, Kennedy avoids the worst part of the final battle and is basically a delivery girl who turns up right before everyone decides to get the hell out of there.
Kennedy thinks she's right so of course she wants Willow to side with her but it's not a personal attack against Buffy.
Willow's known Kennedy two minutes in comparison to Buffy, why wouldn't she side with her best friend? The point is that Kennedy thinks she's entitled to having Willow side with her because they're dating. However all we see is Willow being dominated by Kennedy in the relationship.
Yes, Kennedy (and most of the characters let's be honest) are unhappy that they feel like their voice isn't being taken into account by Buffy when formulating decisions etc. Kennedy does think that Faith will listen to her more than Buffy did but why is that such a bad thing. Of course Kennedy wants to be heard.
Kenendy was brown nosing Faith something chronic before the mutiny. She then just so happens to want to instil Faith as leader. She openly admits she thought she'd get a bigger say with Faith in charge. All this suggests that Kennedy was trying to manipulate her way into a higher position. Consider the fact that the moment Willow and Kennedy are officially "dating", Kennedy is inserting herself into Scooby meetings. None of the scoobies outside the core four got automatic entry, they had to earn their place, so why is Kennedy suddenly there?
All Kennedy cares about is getting a bigger say. After Buffy's departure, everyone is in a high state of agitation and Kennedy's first words are basically about how she should get a bigger say in things.
Kennedy was absolutely out of order for what she said to Chloe however I'm not going to believe that Kennedy was why Chloe killed herself based on the first's word. Maybe if we saw more scenes of Kennedy being rude to Chloe specifically I would call that bullying but one rude comment doesn't cause a suicide.
So I can see how Kennedy is not an entirely pleasant person but she's also not evil.
Kennedy is not the sole cause of Chloe's suicide, but she is very likely the straw that broke the camel's back. That final thing that pushed Chloe over the edge so to speak. The point isn't whether or not the first is telling the truth, it's the fact that Kennedy doesn't even question whether it is her fault. Another character can reassure her she's not to blame all they want but Kennedy should've had that moment of doubt like a normal person would, even if ultimately it was decided that Kennedy wasn't to blame. As it stands, it seems like Kennedy doesn't think she did anything wrong with the way she treated Chloe.
