OP, I'm sorry your thread has turned into this. Just do the best you can do for your puppy.
I respectfully disagree with amputation being wrong if that is all one can afford. 'Personally', I would not send a dog to rescue for this. I'd reserve that for dogs that are suffering. Rescues are overflowing as it is. Many are overcrowded, don't have adequate funds, are behind on vet bills, etc. There are constantly cases where owners can't pay for testing or the very best treatment. Although these cases don't tend to be as drastic as amputation, some are very serious. Sometimes owners have to choose second best treatment or testing (skipping xrays even if there may for an obstruction..which could lead to intestinal damage and death, for instance). If these animals were all sent to rescues instead and decisions were not made based on money, there is no way that the shelter system could keep up. There are millions of animals euthanized yearly in the US as it is. There is no reason to add to this if the owner can provide reasonable care.
I understand if an owner would prefer to surrender, but I don't believe they should feel guilty or judged to go another way.
FWIW, I would rather lose a limb for financial reasons than be separated from my family forever just to get a surgery. Then again, we are very close and would do anything to stay together. Furthermore, we don't make decisions solely on our dogs. Life is much too complex for that. They are always cared for and are not suffering. That does not mean I am opposed to second best treatment options at times. Also FWIW, most or all vets I know feel similarly..as do many techs.
Cost effective options are offered by vets all the time. And the amputation option is one of those. It is not the same as a human getting an amputation. Whether or not people like it, vets do it. A lot of general and ER vets are not into recommending rescue probably because they would be sending dogs to rescues constantly. So if it is between fixing the leg or euthanasia, of course some will offer amputation.
Actually, if it is a salter fracture in a young pup, the damaged growth plate can prevent the leg from growing resulting in one leg longer than the others...even sometimes with surgery. The older the pup, the better things are. So surgery can end in problems too or even failure and you are at square one. That is NOT to say that I think surgery isn't needed, but a lot goes into this.
OP, I would talk to your general vet and one or two orthos about surgery, pricing, alternatives, and if money is a problem - amputation. You can ask if in their opinion if is horrible to do. Yes, if something goes wrong with another leg there will be big problems. That, IMO, is not a reason to rehome.
I'm sure the ER vet would have given you a timeline for getting it repaired. Generally, waiting more than 2-4 days is not a good idea. If it is a salter fracture (growth plate), they are generally best fixed as soon as possible. The upper part of the leg is harder to immobilize, but if it is the lower part generally a vet can Robert-Jones it until you get to the ortho.
Not everyone can shell out thousands. And I don't believe that only those that will max out their credit cards or those able to spend five grand a year are good owners. I used to hold similar positions to those on this thread. ...then I started getting involved in the veterinary field. There is way more to vet med than animals. There are many variables. The majority of owners cannot afford the best of the best. I don't think people realize how many more animals would need homes if all these owners gave them up. After seeing every third or fourth animal in the ER euthanized at times, my thinking changed on this topic. If an owner is doing their best and the animal is not suffering, I consider those animals blessed.
I wish your pup the best.