Should I write a letter to the woman that had physically assaulted me?

I know it's an odd question but it's something I've been thinking about quite a bit. I've already asked some family members and friends who know about this but I am still very unsure and need some advice.

The story starts 2 weeks ago when I was living in a small town with my boyfriend in his sisters' and her fiances' house. We were all living together in a trailer park where rent was affordable for everybody and we weren't too worried about payments, (The sister and fiance have outstanding debts, but that wasnt mine and boyfriends problem, they had that long before we moved in) but they decided to move into a house that was well above our price range to pay for and it caused my boyfriend and I to become very stressed about money.

A side from financial stress, his sister isn't a good person in general. She beats animals (I've seen it with my own eyes), she hits people, she doesn't treat her 1 year old well, she lies to make herself look better, so on so on. I started to see all this come to light about a month into living there when I found out she was bad mouthing me and making up excuses and lies about me to my boyfriend's parents saying I do nothing around the house (even though I cooked food for all of us most of the time and watched her kid for her anytime she asked) a long with some other nasty comments and lies about me.

We were all high one night and a little kitty she had (4 months age at most) was a little too hyper and accidentally scratched my jaw, I thought nothing of it since she was only playing. The sister picks the kitty up by the tail, and grips it by its neck so hard that she gets incredibly scared and peed on the sister, which made the sister toss her to the concrete floor. (In the past shes also whipped the kitty down a flight of stairs to the concrete floor on the basement, the kitty didnt come upstairs for a week after that.)

After that happened, the sister was saying that because the kitty had done that (was also clawing and biting the sisters hand trying to get away from fear) that they now could not keep her and would have to throw her out in the -15°C weather or shoot her to put her down. I told the sister she shouldn't do that to a little kitty, she doesn't deserve that and she doesn't deserve to be abandoned in winter or shot dead. The sister is also one of those people that can never be wrong and was telling me to get out of the house. At 1 AM, high as hell, in -15, in a small town, nearly 100km from any family or shelter where I would be welcome. We argued, one hour later we all went to bed, we were all high.

Fast forward a few days later, she called her fiancees' mother to get me out of the house, dont ask me why she only did that days later, he thought process in general is fucked. I tried to explain to the mother that I had only disagreed with how the kitty was treated and that I would have nowhere to go; but she only stuck to the one side. At this point the sister is yelling at me telling me to get the fuck out as I'm gathering my things. Its pissing me off so I start giving her attitude, along the lines of 'I dont care you're kicking me out I was going to move anyways, this is just helping, thank God I'll finally be out of this shit town' things like that.

The sister is 22, I'm 18, I thought the sister would be smarter than this. As I'm putting on my boots, reaching down to grab my bag, I slowly get back up and the sister punches me in the face. My boyfriend sees, tries to gather his things so he can leave too. Tries to call the police because I got hit, and ends up getting swarmed and beaten by the sister, the mother, and the fiancee. After it's all gone down, police was called and all were questioned, no charges pressed, we got some of our stuff (to this day some of it the sister is hiding and not giving back) and now my boyfriends' family plus the sister are expecting me to apologize to the sister.

My boyfriend knows I have no reason to apologize for the fact that she hit me. If she ended up never hitting me or my boyfriend and let us take our stuff and left, then yea I would've apologized for what I was saying; but getting punched changed the whole scenario.

I do want to try sending the sister a letter explaining why I will not apologize, unless, she apologizes to me first.

I want to write a letter and send it to at least try and patch things up with my boyfriends' family (I more so want to make things better with his parents because of all the lies that were told to them about me from the sister) but I can't do that until I talk with the sister. I want to talk to his parents and tell them what shes saying isn't true, but they're taking the sisters' word over mine, despite them knowing how she acts (even his mom told me a month earlier that she's always been this way).

So question again, should I bother writing a letter to the sister explaining my point of view, or should I not bother and only patch things up with parents?