I'm sorry about little Eli.
If this were my dog and there was any way possible that I could afford it, I'd be doing all that is possible.
Liver disease is not a death sentence.
The stones are most likely secondary to it.
If you take care of the stones he has now and take care of the liver, maybe the stones issues will go away. The vet cannot possible tell you it is liver shunt by one blood test. If they say they can, I think I'd find a new vet. A pre and post meal bile acids test sent to a lab is a good clue but diagnostic imaging needs to be done or a Protein C test. MVD (small shunting throughout the liver) can be managed by diet and supplements. Intrahepatic shunts (shunts inside the liver) are hard to get to and probably can't be fixed. These dogs would be managed also. Extrahepatic (outside the liver) shunts can usually be repaired but problems can develop after surgery. In a young dog, it is most definately worth a try.
Why doesn't a Yorkie have a good chance of making it through three major surgeries? IF the right anesthesia is used and the right pain meds (absolutely no NSAIDs), they can do very well with liver disease and surgery...
Don't know much about hip problems but I think I'd consult with an internist about the liver issues and see when this surgery should be done.
University of Tennessee (best place to have liver shunt surgery done) is probably the cheapest (under $2000). Corness is another excellent place and may be cheaper than $3-5000. That is waaaay too much in my opinion.
Hope everything works out for you.