As it sounds like you are now doing the most important thing is to manage her first

For a dog who has injured other dogs and snapped at people she should never be free out of your sight
You feel her quality of life is reduced because she dosent have so much freedom now, but it is more than likely all that freedom was actually stressful for her, she was having to patrol and see off strange dogs and work with no direction from you

Personal I would build a strict routene with her so she does not have to have that kind of stress and responsability

Imo she is an old lady and not worth a long socalisation programme

Keep her secure when you can't supervise her
Walk her places she is happy, unstressed with no small fuzzies to chase
If she enjoys chasing play with a ball or something
Train with her as she seems to enjoy it

Keep her seperate from dogs you worry she will fight

Quality happy time with her instead of hours of stressful running about

Brill post. Agree with everything BenMc says She's an old lady, try and enjoy her. I'd like to see a photo, I bet she's pretty.

I can`t help feeling there is a huge difference between the USA and the UK as far as attitudes to dogs are concerned. I was frankly shocked that you have allowed your dog to injure other people`s pets - and that you feel money can compensate for it.
The dog has been allowed to get like this over time - and that is down to you. Now you have children you suddenly see what you have created - an aggressive and dangerous animal.
It might be possible to rehabilitate this dog - but if you haven`t done it over 11 years I don`t see you being able to now without a complete change of how you manage your animals.
I suggest you find a good trainer / behaviourist (one who does not use aversives as that will make the dog worse) and work with them to protect others from your ddog and bring her under control. In the meantime you MUST provide a secure run and also muzzle her when out.

the dogs I paid vet bills for who were badly injured were both on my property when they shouldn't have been so I'm not quite sure how I could have prevented it. She is now in a very sturdy fenced area where no other dogs can get in. She's always stayed in her underground fence but of course other dogs won't stay out. I am all about taking responsiblity for myself and my dogs but when people let their dogs onto my property with 4 huge dogs I feel like I'm doing more than my part in paying the vet bill. Besides it's not like I live on a postage stamp lot there's a small creek and grove of trees between these neighbors and my property line.

Of course one does have to take account you arent in england, but in a country whereby open and/or rural properties arent standard. I have lived in denmark and new zealand where what you explain about your property wouldnt raise a eyebrow when it comes to dogs.
So fair dues if the dogs came into your property, so you did right with the vet bills.
And there is no difference between UK and USA when it comes to owners whom know they have problem dogs, yet let stuff happen.
But having said that, everything in balance, and i would say that if you knew you had a dog with these issues all these years.....and its quite well known in America that the chow is one of the 'dangerous breeds' (not my phrase) when it comes to bite stats etc, so if it had been me i probably would have fixed a secure area a long time ago, or if letting my dog run the bit of the property that is free range, then muzzled accompanies him and muzzled him.
And got to know my neighbours so they know about my dog.
Like you say, its the american countryside, so if you let your dog free roam in such an environment, i should imagine that others do the same.....local culture n'all?.... so you could have probably anticipated that these dogs would crash into yours at some stage.
So i would still say you have a moral obligation to take measures to protect neighbouring dogs.
I'd re-read smokeybear's post, lots of great insights there.
I think its not so much an issue how can you 're-train' your dog, its more an issue of your own expectations and management strategies.

If their dogs can get in then yours can get out. If you know your dog is aggressive it is your responsibility to protect others, not theirs to avoid you,