Okay= first of all relax. They will become friends, but we need to control the bosterious baby in the pressence of our older little girl here. She doesnt understand he is a baby- she just thinks he is big and boysterious and no adult manners. I would suggest, when the puppy is quieter, holding the puppy, just let her get to know him. Control the situations where he could run at her- he just wants to play, to her it looks like a flying clumsy tank coming at her.
Collies are normally pretty docile but that is as adults. As youngsters they can get pretty wild. I actually like your idea of seperate yards to go out. It gives the puppy time to play and gives her a repreieve from his antics. Use inside the house to not only teach him play is for outside but also for them to become friends. This is going to take time.
Also remember when you scold the puppy, the older dog thinks- " see ever since this thing came in here "everyone gets in trouble". There fore try more distraction to the puppy . Start training clicker training. With the older dog, this should be easy. Tell the cavalier to sit, click and treat ( I use cheerios because they are small, quick and they wont fill up on them). Meanwhile work with the puppy. First click then treat, click then treat, - when the puppy understands that noise means something good, start with sit, click treat. Now you have both of them together- with their focus on you and not each other. Say sit, click and treat ( adult dog gets the treat first but be quick..)..
Getting adult small dogs, and big dog puppies will work with some work on your part. I use to have a Affenpincher, a 8 year old with young shepherd pups. Allow the older dog to correct the puppy " leave me alone" ( she wont hurt him- its mostly display) but use distraction as much as possible.
Remember to feed her first. Also if the puppy has to still get extra meal like lunch, seperate some of her food so she can eat when he does too. It wont take long before she realizes that in her mind she gets " more" with this guy around..