I am so sorry you are having to go through this experience. In response to your question, when we see patients die so quickly they generally have eaten the poison for a while and were having coagulation disorders yet they were not clinically ill. In other words, the patient already had a problem but was showing no symptoms.
It is also difficult to establish an exact time of ingestion as there are so many different types of anticoagulants with a different set on action and potency. We also have to consider the amount ingested. For example, many of these poisons will take 1-3 days before we can detect evidence of coagulation problems in the blood. But, the patient may take another few days before they become clinically ill. Depending on the amount ingested and type of poison some dogs will not become clinically ill whereas others will. So, as you can see it is difficult to prove right now that your dog took the poison at your vet's.
Finally, it is also important to remember that dogs do develop coagulation disorders. For example, vWD (Von Willebrand Disease) can cause similar symptoms. Though not uncommon in dachshund breed, but, it can happen. There other disorders or factor deficiency that can occur in the patient leading to coagulation disorders. So, if the ER vet did not find actual evidence of poison in the patient and is solely making his recommendation on a coagulation profile I think ER vet is not considering pathological coagulation disorders as a possibility.
In conclusion, I think that your dog may have appeared to be clinically ill quickly but this may have been going on for days prior to him becoming clinically ill. In addition, we need to consider that there could have been other factors/diseases that could have played a role into a coagulation disorder. So, unless your family vet admits that the dog did take the poison in his facility it is difficult to prove this. I realize that this answer may not be entirely to your liking, and I regret being the bearer of information that you really don’t want to hear. But it would be unfair to you and unprofessional of me were I to provide you with anything less than truthful and honest information. I hope you understand.
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