@Sciencemama
As you know 13-year-olds are not easy, neurotypical or not. You can try taking a more active role with your partner in her education and making her understand what your rules are. It requires tons of patience, you should outline your issues to your partner with a degree of diplomacy, her father might be a bit defensive at the beginning, but if both are reasonable a consensus should be reached and a plan put in place, both have to work on this, if not it will be a waste of time.
I am raising my granddaughter, she is non-verbal, so communication is not easy. In my case, my former partner was not able to deal with her so at the end we moved out.
You know your limitations, it is your decision if you put in the additional work or not. If you decide to go forward clearly define what you want to achieve and in what time period. Make sure your partner understands this.

@Sciencemama
I'm sorry for what you are going through. Although it is a difficult situation, it seems that you are very clear of your limitations and every member in your family too.
Austie people don't do things because is common sence or best for everyone. Must teens don't regardless of their mental health anyway. That is why they could be annoying even to their parents sometimes. Austies learn as a form of habit. They have to do it millions of time so they could create the muscle memory to do it without thinking or in their case without being reminded. Sometimes, they never get to learn those tasks. They need someone patience enough to remind them without getting upset until they do it on their own or for the rest of their life. Not a simple task.
The problem that I see here is that you are sailing this ship alone. Somehow you became the single mother of your partner child. It fustrate me just thinking about it.
In a ideal situation, you and your parents should have had a plan in how to deal with his child behaviour. Because, you are not her mom, you cannot be the diciplinarian. That is your partner 's job. However, they are in your home whitch they need to respect or at least make an effort. In other words follow the rules. If you cannot get your partner on board in the social education of her own child, I don't see much progress in the situation. You mention that he has some difficulties aswell, whitch it might makes it more difficult for him to comprehend your situation. And even if you do, he might have a hard time following the plan; the child may never act without being reminded and you would hardly get any appreciation from neither of them. You would need in creating a bond with his child too and I don't know if you would be able.

I 'm so sorry if I have offended you in any way. I'm sorry you are going through this.

Thank you both. I am having to do some shopping to do in a moment so I can't make a lengthy response but I will definitely keep these ideas in mind. Thank you for your input and perspectives.

@Sciencemama I’m big on being honest, especially when it comes to cohabitation. Would it be difficult for you to tell him what you’ve shared here? It sounds like his daughter may be missing some basic skills that are taught early on. Or perhaps this is her way of controlling/manipulating her world-in one she may not be pleased with. She may not like that she has no choice but to be there. So she may behave accordingly, because her father supports her, and if it gets on your nerves, she wins. Behaviorally, if that’s the case-Patience on your behalf is the answer, while also discussing with your partner how you feel, that basic skills can and should be learned by repetition. Look into a token economy system to reward her everytime a desired behavior happens. This may help. Update when you can!

One of my granddaughters is PDD-NOS. She was nonverbal and in diapers until 4. After 2 years in a learning center, she entered public school. One area few people discuss are children who are ODD and/or violent in their autism. I have found her rage had much to do with her inability to communicate. The rage was epic. I helped her mother raise her because the father was disinterested. She spit and bit us, screamed we were abusing her so neighbors would hear, and generally had a violent meltdown or two every day for years. That takes an emotional toll. Now at 17, she has learned many coping tactics and is learning how to deal with letdown for when she gets a job. It can still cause a meltdown, but if caught early enough, we can talk her down (maybe one or two a week). As with most people with Neuro problems, she is also very intelligent. Our loved ones are conundrums that outside people cannot understand. My daughter and I separately suffered PTSD from sexual abuse, which was compounded by years of my granddaughter's abusive behavior. My wish for you is to find some peace for yourself and for her. Remember, it is her behavior you really disapprove of, not her.

Thirteen years old is a notoriously difficult age for human beings. (That's exactly why separate middle schools were instituted! LOL) However, if cleaning up after herself is not ingrained by her age, reminders of duties are necessary. Sometimes verbal commands work; others need a chart. However, at this age it's very likely to be because she just doesn't want to! Training her for independence cannot begin too early. Enlist her father's help in preparing her for life after he is gone. It is his duty as her father. I hope you don't have to go this alone. It's not your job, its your choice. Your family is lucky to have you! Peace.