OP - this is what I do for a living...
So.. you've bought from a crappy breeder, who won't take back, which makes that option much harder as now we're talking rehome via a rescue (they're all full) or privately rehome (takes a while unless of course you just irresponsibly hand over to the first person who shows up)...
Point being this puppy isn't going anywhere soon.
Lots of children, NT or ND... are horrified by the reality of a puppy.
In theory, a puppy is a cute, snuggly, best friend who always wants to do what they want to do, play games, sit and watch them play, snuggle, etc. Never any disagreement, never any competition like there would be with another child, its all just lovely.
The reality is that your child has got a needy new sibling who is NOT fulfilling any of their expectations at all - they don't listen, don't want to play her games, don't want to watch her play, do want to bite her, etc etc..
And she can't communicate that well so she gets frustrated and stressed at the puppy themselves and of course then gets into trouble for THAT so.. obviously the puppy is to blame, demand the puppy is removed.
Separate puppy and child.
Use a room divider where necessary so they're both in the same room, so neither is missing out on company, interaction etc, but they can't annoy or hurt one another.
Reward the absolute shit out of either of them for IGNORING the other - sounds counter intuitive I know, you want them to like each other but that route means them being too close, physically, it means big risk of one hurting the other and fall outs and so on.
Rewarding them for ignoring each other, choosing to go away from one another is much much safer.
Once you have the dividers set up and some sort of routine in place, you can keep explaining to your daughter that the puppy lives here too, what the rules are around the puppy, where she can go to take herself away from the puppy, how she can ask for an adult to help etc etc.
I would rehome this puppy though.
It is a red flag that the breeder wont take back and struggled to sell.
It is also a red flag that this puppy is apparently so chilled - after the first night, most puppies are bouncy and into everything and the level of laid back you describe makes me suspect something is wrong tbh.
Whilst I can see how pets can help people with autism, unfortunately I very often see dogs/pets really suffering as a result of being that 'help' and I don't think that's acceptable.