
Hi
Do you know anything about the history of your dog? Was she run free before you got her? Do you know what cues the previous people used or any info at all about her? If so, you may well have a foundation to build on which could be good news.
If not, train her to recall to you in the house first and then in the garden - rewarding her either with a titbit or a game with a favourite toy. If you can then find somewhere like a tennis court that is enclosed to practice your recall in, that would be great. Then slowly build up to gamey ground. At each stage you need to build in distractions, so even in your living room you need to be able to work towards calling her away from her favourite toy or some other family member.
Make sure she gets loads of opportunities to interact with other friendly dogs in secure areas - even if only in your garden. I know that you are worried about her running up to other dogs but by restricting her access to others of her own kind, you increase their scarcity value and will make her even more determined to run up to them. I found the best way to teach my pup to stay close and wait until I told her to go greet was to spend the morning with her and invite a load of doggie friends around to play. By lunchtime a) she was tired and b) she had got the obsession out of her system so that when we later spotted an elderly lab walking across the field she was not hell bent on legging it over to say 'hi' but was prepared to listen to my stop whistle. I then leashed her and walked over to the lab and asked if she could say hello and then the reward was being let loose again to play once more. Do this often enough and eventually you don't need to leash them, but can either keep them on a 'stay close' cue or keep them focussed on you by playing with a ball or whatever.
I have GSPs so have the same worry as you about chasing rabbits and pheasants etc. You will never stop her hunting them so you need to make yourself in charge of the hunt and be part of it. That way you can teach her to hunt on cue and also to stop hunting on cue. You are then the focus of her life......because you give her permission to do the one thing she desires - hunt! - and are not always telling her to stop hunting.
It may sound a bit gruesome if you are not into hunting/shooting, but what guarantees a recall on gamey ground with my 20 month old pup is a bit of cured rabbit skin which I keep soaked with rabbit training scent. I have this on a piece of string and if I need to recall her in a high distraction environment running around with this in her mouth is her reward. She is not food focussed at all.
You can buy both the scent and ready prepared skins online from Turner Richards or any other shooting shop.