I'm so sorry about your babies.:cry2
Sounds similar to what Dora and Gir had. They were given to me when they were just old enough to open their eyes (guessing a little over a week due to the owner's story and their size) and were emaciated because their mom had apparently been too sick to make much milk before she died. That was a Tuesday, that Saturday Gir had uncontrollable (no sphincter control) green mushy diarrhea. We couldn't get him to swallow anything at all and he died.
The next day Dora got the same problem and also appeared to be leaking urine but it was hard to tell. We were able to get her to swallow a little bit, so we were able to pull her through with Pedialyte mixed with healthy cecals from another rabbit and a tiny bit of Critical Care, and Benebac. We stayed up all night with her, kept her warm on us as she preferred that to the Snuggle Safe, and gave her the oral liquids every 15-30 minutes. By morning she had perked up,regained control of her body functions, and her poops had some shape to them. A vet gave her sub-q fluids on Monday and Tuesday. By the time she saw a vet there wasn't any need for antibiotics any more, according to them.
We had multiple diarrhea problems with her that required vet treatment. She had issues with Clostridium (toxin-making nasty intestinal bacteria) that she got antibiotics for and also needed GI mobility drugs to keep her gassy cecum working better. And Benebac regularly every day, plus Critical Care which includes probiotics in it. If we had been able to get Clostridium medication for Dora (and Gir) immediately we probably would have had an easier time, but the emergency vet clinic didn't have a clue what to do and weren't worth the 1hour drive considering they can barely treat adult rabbits.
So the answer is, sometimes they can be saved. Obviously Dora was slightly older than your babies but she was far less healthy to start with and has being handfed, which makes them more prone to diarrhea. My vet made sure I knew how very low her chances of survival were so I wouldn't get my hopes up. It took literally round-the-clock care from us plus veterinary attention. She was sick on and off for weeks, but has been healthy ever since. *knock on wood*
The cold-but-alive kit might have had other problems going on than just being cold. Maybe it's organs had already started to fail, maybe there was something wrong with it genetically or the way it was formed. There's really no way to know.
There's a discussion here on euthanasia, including a link to veterinary information on it and discussion of many different types and how appropriate they are for various sized animals:
http://www.rabbitsonline.net/view_topic.php?id=43907&forum_id=8