When we take on a rescue dog we can sometimes take them into our homes feelin sorry for them. This a huge mistake as they read us as being very weak. From day one we are viewed this way and creating a leadership role becomes very hard.
I suggest you follow the thread I have posted on rebalancing the leadership roles within the house. Your dog seems to have very little respect outside the home so i think it might be a good place to start.
Recall should be done with a very long leash. It allows the dog to roam but you have control in retrieving it.
Remember you picked a collie, and all it's behaviour really is just an exaggerated natural instinct.
Laying down suggests it's herding instincts in use. does it show any aggression whilst doing it?
Also when your dog does this do you stop turn and look at her?
If so it's leading the walk. I do You follow!
When the dog drops try to keep moving. If this doesn't work catch the dog before it drops and set off at a sprint past the other dog. Key is to interupt the dogs pattern of behaviour. Dogs can't think of two different things at once. if shes running she might stop dropping.
Also if you can catch your dog befor it drops spray pet corrector near her rear end. this too acts to interupt behaviour.
Remember keep moving forward, you'll most likely add to this problem, because every time you see a dog coming you expect it to do it. Dogs read us and she 'll think that's what you expect. Say to yourself" see dog keep moving" over and over.