possible controversial take...
So Sam not looking for Dean whilst he was in purgatory was a big mistake on Sammy's part. Like Dean said once he returned, they've always looked for one another!
So when Sammy hit the dog he, being Sammy, immediately took him to a vet to get the dog help. Amelia had instantly started in on the unneeded guilt trip Sam did not need at that moment. She literally guilted him into taking the dog when he really was not equipped to do so.
So point bring I personally think that the whole Amelia plot only happened because they both felt pity & obligated to the other & I mean they were both very lonely people. Thats not to say I don't think their feelings weren't real, just did not have a good foundation.
And on top of all this, like Sammy said when Dean came back, he was under the impression he had lost his last & closest family member.
