Schools don't usually pick up on autism/ADHD etc. IME. They never picked up on it with my DC, even after I have told them they have been diagnosed they look dubious/confused and say "Really? I never would have thought..." IDK why because DS2 in particular hits every single stereotype you could imagine including that ADHD medication calmed him right down, and DS1's teacher turned out to have rated him far worse on the questionnaire than we had on the parent one.
Children with ADHD have specific behaviours which are almost perfectly honed to get on an adults' last nerve. There is actually research showing that parents are more reactive towards the ADHD behaviours. That is not to blame the child or parent, it is helpful because it makes the picture clear - what commonly happens is that what's called a coercive cycle forms.
The coercive cycle goes like this:
Parent asks child to do/stop doing something (a reasonable request)
Child refuses/ignores
Parent repeats request, possibly escalating to warning/threat
Child refuses/escalates to challenging behaviour (tantrums, shouting, "attitude", etc)
There may be further cycles of the parent getting more angry and the child getting more defiant, but the outcome is that things keep escalating until either the parent gives up and drops the request or the parent succeeds in scaring the child into compliance, which could involve an action they feel guilty about such as shouting, name calling, physical violence, damaging property or giving too extreme of a punishment.
Over time the pattern becomes more entrenched, so you both more quickly escalate. This pattern is unintentionally extremely reinforcing for both parties, because the preferred outcome for each (avoidance or compliance) happens some of the time and this gives you the slot machine effect which is even more reinforcing than an outcome which happens consistently. So once the cycle has started it is highly likely to continue unless something interrupts it.
Reinforcing does not mean either of you enjoy it. Most parents stuck in this pattern hate it and wish it didn't have to happen that way but it always seems to anyway, and they don't know what else to do aside from stop making requests of the child, which is not usually possible or they are already partially doing anyway.
If it gets very bad you can also enter a state of Blocked Care which is where you start to lose empathy for the child, dread interaction with them and see all the behaviour as an attack or a sign the child is out to get you/inherently bad. I don't know if you are already here but you did describe DD as the spawn of Satan, I realise that could be tongue in cheek. FWIW the "tips" on the leaflet are good but they come across as this simple easy thing you can do whereas they are actually much more in depth than the one sentence on a leaflet suggests. The important things are improving your own support network, seeking professional support and looking to interrupt a coercive cycle if this is happening.
In terms of interrupting the cycle there are parenting things you can do - the PACE approach mentioned in the Blocked Care leaflet is one (it is a specific thing you can also look up), what also helped me is approaches which understand dysregulation and what it is and what to do (Big Baffling Behaviours, Mona Delahooke, Conscious Discipline) or you can replace the escalation with a very boring, generic consequence which is so small you can repeat it all day and never run out, while focusing on encouraging/developing positive opposite behaviours (123 Magic, Triple P Parenting, Who's In Charge, Incredible Years). De-escalation and reducing in-the-moment demands (Low demand/PDA approaches, The Explosive Child, NVR) are also helpful to interrupt a coercive cycle.
IME you can use several of these things together. The main thing is that you reframe her behaviour from being an uncontrollable, unbearable emergency, to being something where you understand what is happening and how to handle the situation. Having a set guide of what to do instead of escalating can be huge because if you don't have anything to do you will likely default back to that automatic response.
Delayed speech development is a huge red flag for other issues particularly in the area of social-emotional development. It's frustrating you haven't received support and input with this. I know our system is completely overloaded and that's not your fault. Having family members on the autistic spectrum also means that it's more likely than average your DD could be autistic or have ADHD, even if she doesn't present anything like your family members. They think that there are multiple genes involved in autism and of course these genes pass down in families. It's only when someone has a certain amount of the genes that they express as autism so it's possible to have quite a few of the "autistic" genes and not be autistic. Family members of those on the autistic spectrum also have more autistic traits than average although again may not be autistic themselves.
< she doesn’t use her words when she’s upset she just makes noises at me and stuff > - this to me is a huge sign that she is not really "upset" but actually dysregulated in these moments meaning she's actually struggling to access the brain regions which will help her with calm and rational responses. Talking to her in those moments is about as much use as talking to a wild, snarling injured animal, it's all about body language and using the environment to convey safety. DS2 is very much this way and even so with language. He loses the ability to hold a conversation when he is dysregulated, he'll either make nonsense sounds or put on a silly voice and if he does talk, silly voice or not he's not responding to what you said or he will respond to everything with the same repeated phrase which doesn't necessarily make sense. He is diagnosed ADHD and we think he is likely to be autistic as well but the assessment he had so far was inconclusive.