My Dogs fight with each other-don't want to get rid of them but they can NEVER be together again?

Two Dogs 1. Grace, Spayed Female, Beagle, 2 years and 5 months old, got her at 7 weeks old from an ad in the paper 2. Gert, Spayed Female, Mix Breed - possibly Pit bull/Boxer, stray rescue - 2 years and 6 months old (estimate), got her at (approximately) 4 or 5 months old from a rescue organization that... show more Two Dogs

1. Grace, Spayed Female, Beagle, 2 years and 5 months old, got her at 7 weeks old from an ad in the paper

2. Gert, Spayed Female, Mix Breed - possibly Pit bull/Boxer, stray rescue - 2 years and 6 months old (estimate), got her at (approximately) 4 or 5 months old from a rescue organization that pulled her from the county animal shelter - she was on death row & I had to drive 3 hours (one way) to pick her up

When I adopted Gert, I took Grace with me on the car ride. The rescue people were at the animal shelter. They had me introduce Grace and Gert to see if they would get along - they were both about the same age and still puppies - they got along very well immediately and I took Gert home.

Grace, even tho she is physically smaller always seemed to be number one in pecking order because she was more confident.

They were like best friends and sisters and played together.

They had some difficulties along the way but it wasn't until they were about a year old that they had a serious fight. We changed some of our routines with them in order to prevent this from happening again. Mainly keeping them separate when we had company over bc they really seemed to want to fight over attention from "new" people.

They still slept together every night and played together all the time.

They had about 4 or 5 of these pretty serious skirmishes over the next year or so - but they were few and far between - we worked out a way to separate them quickly - i would hold Grace's mouth shut while my boyfriend opened Gert's mouth and unclamped her from Grace and then we would keep them separate and let things cool down.

We tried this spray that you are supposed to spray on fighting animals but it didn't work. I emptied a whole can right in their faces and they didn't care.

So we have been in a kind of limbo, not knowing what to do.

Then a month ago - they had an extremely serious fight. I was alone. I did everything I could to break them up but when I would get one loose the other would start it up again. I mostly worked on trying to free the Beagle from the Pit and then getting the Beagle inside the house to separate them. But the Pit snatched the Beagle out of my arms. I also got bit many times by the Beagle. While the Beagle is being bit she thrashes her mouth around in the air biting at anything. So while I was working on removing the Pit, the Beagle bit me many many times until I couldn't move my hands anymore and I gave up.

I thought the Pit would kill the Beagle.

I went to the urgent care.
Then we came home and took the Beagle to the emergency vet.
She is recovered now but she was seriously injured.
The Pit had some bites on her face and eyes but was not injured as much bc she is so much quicker and stronger.

Since that fight we have kept them COMPLETELY SEPARATE.

I feel we can NEVER put them together again because I don't want to see the Beagle suffer like that again. She had cuts all over her arms, legs, and throat.
I also don't ever won't to have to try and break them up again. My hands healed too but it could have been much worse. It is very scary to try and break up dogs fighting.
I wish I would have had welding gloves on or something like that.
A lot of people say to try a hose or bucket of water but the dogs don't even notice things like that. They are intense.

Both of them are extremely sweet and loving dogs to people, they love us & I love them both.

NOW HERE IS THE QUESTION:

SHOULD I GET RID OF ONE?
WHICH ONE?
SHOULD I TRY TO KEEP BOTH OF THEM AND KEEP THEM SEPARATELY?
ANY OTHER IDEAS?
Update: Additional Info:
keeping them separate is very difficult, whichever dogs is alone cries
Update 2: Picture... show more Picture Links:

http://www.flickr.com/photos/40351750@N07/5221003341/

http://www.flickr.com/photos/40351750@N07/5221003297/

http://www.flickr.com/photos/40351750@N07/5221003247/in/photostream/

http://www.flickr.com/photos/40351750@N07/5221601770/in/photostream/

http://www.flickr.com/photos/40351750@N07/5221601752/in/photostream/

THANK YOU ALL FOR ANSWERING
Update 3: PAT K - water doesn't work, at all.
they are in a home with a big fenced yard, they get a medium amount of exercise but could get more - i agree that tired dogs are good dogs
Update 4: F D
that is true about breathing rights
Update 5: BOBBIE L
sorry about the length, i tried to edit but....i couldn't sorry
this is really hard for me
Update 6: Oregano1

We think the Beagle is the instigator
Update 7: thanks Oregano1
i appreciate the time you took-you have good info
Update 8: CHARLENE

Thanks Charlene
10 answers 10