I know you said you’ve stepped away from the thread, but I’ll comment in case you’re still reading.
This really does all sound like perfectly normal puppy behaviour. Try to imagine you had a brand new, tiny, 9 week old puppy who was displaying this behaviour. Would you be as concerned? I know your pup is older and bigger, and that makes it seem a bit scary and inappropriate/naughty, but it’s highly likely she didn’t get anywhere close to the correct training and socialisation as a young pup. So now you have an adolescent pup who is dealing with all that the teenage years bring, without having had those important boundaries set early on. Adolescent dogs are a pissing nightmare at the beat of times, so it will be difficult for a while.
A few reassurances from a fairly experienced dog owner;
The growling when pulling at your sleeve is almost certainly normal behaviour. When pups play, they’re acting on instinct too. It’s not an aggressive growl, I always think of it like an excited toddler squealing.
The jumping up and nipping also sounds completely normal and is something she will grow out of. I know you’ve already said you won’t, but spraying isn’t a good idea, no matter how effective it was.
Your kids being wary or scared of the dog - explain to them that she’s just excited, confused and hasn’t been taught the rules yet. Then try to keep them separate for a while whilst you work on the behaviour. Yes it’s disappointing to kids who were excited to get a dog, but as you said, they’ve already waited a long time for this dog, a few more weeks/months whilst you train her won’t hurt (as disappointing as it may be), and will be so worth it when they have a polite, well behaved dog to pet and play with. If you can, try to put your kids’ disappointment to the back of your mind and focus on getting pup following basic commands and rules. Believe me, I know how hard this is as I’ve been there, a long time ago we had to do the very same thing with a much longed for rescue and it upset me greatly to see my dd’s disappointment. She got over it and it was all worth it, they were best friends for that dog's whole life.
It will get better. Try to stop overthinking everything and assuming everything is a sign of an aggressive dog. I’m almost certain from what you’ve written that that is not the case. With the probable lack of training and socialisation as a very young pup, you’ve essentially got yourself a toddler mixed with a teen. It will pass, stick to positive training methods, be consistent, and you’ll come out the other side with a lovely dog, wondering what on earth you were so worried about.