Thanks all for the responses thus far.  I really want to stress we have tried every range of emotion, every tone, being firm and serious, being lighthearted.  I have not even begun to detail the behavior beyond this.  A few years ago, SS had hit a neighbor's dog with a shovel because it was near our fence (I was not dating my partner at this time).  SD once was scratching and touching SS's legs when they were sleeping together on a vacation in a hotel bed.  He asked her to stop and she wouldn't.  We explained to her why that was unacceptable and would possibly cause her legal issues just touching people without their permission in the future as an adult.  She stood there, no remorse.  She laughed.  She was furious and enraged that we made her sleep on the floor.  I ended up sleeping next to SS to protect him because the whole thing rubbed me the wrong way.  My partner was monitoring her all night. In the same hotel that SS later went on to call "garbage," despite us paying $1000 for a 3-night stay for a vacation for my partner's birthday.  

We took SD to the dentist a few weeks ago, and she was picking at her sweater and destroying the emblem on it.  My partner asked her nicely to stop, she continued, so my partner gathered the sweater and held onto it.  SD came rushing me (in public) and had her fist clenched and got mere inches away from me with intent to hit me but had stopped before she made the next move.  She has a history of stealing items from me, from her brother, both of them like to work together to do bad things together.  We have already applied through our state for disability services for SD.  However, SS did NOT qualify.  They both have been dx autistic and ADHD.  I don't doubt that they struggle internally, but they both like to hide behind their disorders, which we both explain is not acceptable.  Last year, SS had taken a chair and thrown it at a teacher and told them that he wasn't ''doing his f$cking stupid work sh!t" when asked to nicely.  He tried creating shards at school last year as well.  To our knowledge, nothing that extreme has happened this year, but just the same.  The teachers have told us that the kids seem to have improved more when I moved in, so it's very disheartening that this is still ''better'' behavior than prior.  We both used to be highly hands on (partner still is, I just withdrew due to feeling like I was being tormented and borderline abused), always motivating the kids, I would write them notes of encouragement (and still do but less frequently).  We use positive praise.  We had incentives using a points reward system in the house.  We'd award them points for doing a nice thing, doing the right thing, doing a household responsibility without being asked to, using good time management skill, etc.  When they earned enough points we could get them a treat or new toy.  The kids were STILL doing things like this.

My partner takes them out to exercise at the park and they complain or don't want to go play or socialize.  They don't want to get involved in activities at school.  We discussed getting them involved with the teachers already and getting a plan in place for next school year in regards to that.  We keep trying.  We asked them to find some clubs at school and talk to some teachers about joining.  No interest.  Neither wants a social life.  SS yelled at me and my partner once for considering moving somewhere else because he had ''friends'' here.  We asked him if he'd like to hang out with these ''friends'' and he said ''NO."  I suspect these are the same "friends" he was caught doing delinquent things with at school.  They make fun of kids at their school.  SD has been drawing guns in her notebook at school, which my partner has taken to the therapist.  They are supposedly looking into behavioral programs for her.  We also found an drawing of someone who we believe goes to their school.  In the drawing, there was a person laying down with red on their heads, and a gun near the bottom of the page, and I presumed the red was blood.  When asked about it, of course they stammer over their words and SD says, "That's just red hair! You're crazy! That's NOT blood!" 

If someone had a solution that was guaranteed to work, I don't think we'd be here still.  We are really just trying to mitigate the most damage done to other people while holding them accountable and still trying to encourage them where possible.  We don't have many available therapists here in the area.  They've already switched therapists a few times previously.  They get themselves kicked out of activities and camps.  Our local YMCA could not even support them last summer after our interview with them.  They said they would not take them.  They do not and will not comply with authority figures.  We are working on applying for the area's summer camp for those with disabilities/autism.  It's 10 weeks and they have lots of activities.  Last year we tried to apply as well but got waitlisted.  Despite that, I offered to enroll them in swim lessons.  A very firm "NO" and "that's boring!"  Despite all the complaining of being bored.  No babysitter wants them.  We're fortunate my partner's parents watch the kids once every month for our anniversary, for about 3-4 hours.  Even their psychiatrist said that she cannot really do much else at this point and recommends we see a child psychologist per referral.  The pyschiatrist believes they may have conduct disorder.  At the end of the day they are their own people and going to make their own choices regardless of what we keep trying to educate and reinforce.  Hopefully with more context you can understand the severity of the situation.

Also want to make clear we have a calendar on the fridge daily with a few household responsibilities for them to complete daily. Could be to make their bed, do a sweep of their room, take the trash out, even hygiene like wash hair, brush hair, wash their clothes.  They often get enraged if we remind them to brush their hair or tidy up.  Doesn't mean we give in and stop doing it.  We aren't unreasonable and leave some days empty so they can just have fun and take a break.  Me and partner rotate certain tasks like doing dishes amongst us all so they can practice now.  We try to keep them structured. With idle hands, they get into trouble worse than if they were given something to do.  They act incompetent despite us showing them calmly how to do things and breaking them down into smaller tasks to accommodate them.  It has to be intentional because they both have performed XYZ task before, whether in front of us, in private, and/or at school, etc. just fine.  "I don't know how to do thaaaaat" is the typical whine.  We will show them again and they just don't care and get so hostile.  They had prior privileges like Xbox but got revoked due to SS controlling SD's way of playing games and both of them disrespecting the console and remote, often just throwing it against hard surfaces when angered.  They get angry we have parental controls on TV.  They both have the opportunity to watch TV for 1 hour daily, up to 2 hours on weekends.  Still not good enough.  I had Neflix, Hulu, Max, etc. but SS doesn't want the TV any longer because there is no suitable TV show for him.  I told him watch something or don't, your choice.  SD and SS both try to actively seek out disturbing things and get angry we don't allow YouTube in the house for that reason.  They don't WANT to be decent people.  And no matter how much time you devote to them, they need more entertainment.  Boredom is not an excuse to be violent.  We've explained this to them.  I know many neurodivergent kids and adults who don't ever resort to violence or destruction and criminal activities.  I've also engaged SS in helping when we get new furniture so he can tinker and put things together with me.  They are not being ignored or confined 24/7.  It has escalated to this point for a reason. SS and SD both have legos.  They have skateboards, hoverboard for SS and pogo stick for SS.  SS also had a huge collection of toys, stuffed animals, etc. that he never wants to earn back.  SS is never interested in reading a book.  SD is artistic so she has pencils, pens, construction paper, fabric, sewing, knitting all at her disposal.  We buy them something new and next day they want nothing to do with it. Onto the next monetary thing. No amount of money or convincing us ''just this one thing, please'' makes either one happy.

Regarding the ignorance and incompetence, SS forcefully spits out his toothpaste for example after brushing his teeth.  The force is so powerful that it gets all over the mirror and sink.  If we don't point it out and ask him to clean it up, he wouldn't.  He gets mad if we do point it out and ask him to be more intentional and spit into the sink.  They get angry if we ask them to eat over their plates or pick up after themselves.  They often leave pools of water when refilling their water in the kitchen.  SD often leaves toilets unflushed.  SD has dripped period blood on the toilet lid and/or floor and apparently can't see it until we make her clean it.  Again, she rages.  They cannot be asked the most simple of tasks and be trusted to complete them without complaining, raging, lashing out, screaming, kicking.  They destroy everything given to them.  Or SS tries selling gifts to people at school so he can turn a profit and buy something better.  He never wants to hold onto gifts given to him, regardless of the person.  It really is truly this intense and this difficult.  Hourly and daily.