I wouldn't get a prong collar for a dog that's reactive. I used to have a choker on mine and it made the situation a 100 times worse. When your dog pulls the collars tightens and causes discomfort, which she will associate with the other dog, and it will just wind her up even more - which you really don't need.
As for in the garden (yard), keep your sessions out there short and sweet - you will be able to keep her attention for 10 minutes or so - but to keep her attention for an hour is asking a lot. So have a few shorter sessions instead. Keep her a long leash and if she starts pacing - get her excited by playing tug or show her a treat and run off inside, she'll more than likely follow, if she doesn't - reel her in. She'll focus on you more if it's fun
What I found worked with my dog was just reassurance. Could you just sit on your doorstep for instance, or behind a garden gate or on a bench in street where you can see dogs at a reasonable distance. Whenever Cinder's sees a dog, plenty of praise and a treat for remaining calm.
Watch her body language, if she starts to lose control, put your arm round her shoulder and chest, pet her and reassure her. You may think I'm crazy....that's Ok .... but I used to gently whisper to my dog "Shush, Shush, Shush, it's ok" over and over, as I petted him - it worked wonders.
You're going to need a load of patience I'm afraid.
Yeah, I won't use a prong unless I can have a trainer advise me on it. Which probably won't happen. XD So instead, I will work with her on obedience.
I have tried everything you listed as a solution to her issue in the yard, and she really has 0 interest in me when she hears the dog. I will definitely get a long line and work with her on that from now on so I don't have to chase her down and catch her which is causing problems in and of itself.
I'm still not 100% sure what her deal with other dogs is. I can't tell if it's aggression or excitement, since I haven't see her actually interact with another dog yet. The barking/whining is her frustration, since when she is close to what she wants she is calm. At least, this is how she is with my cat. I have been introducing them which she is in her crate and when Lily is close to her she is fine. She is focused on Lily but doesn't show any signs of aggression, just very interested in her. As soon as Lily is out of sight, however, she starts to whine and bark. I'm hoping that she just really, really, really wants to meet the other dog like my St. Bernard did, since working with a DA dog is not something I want to do. XD My aunt will help me with determining which it is once Cinder's out of heat by introducing her to her two neutral and dog friendly labs. Once I know if it's just excitement or aggression I will be able to make a better game plan, but for now I'm just going to work on her focus and OB commands.