So sorry you both had to go through this, you poor things, how scary! But please, do not beat yourself up. Honestly, I think any of us would've trusted that our neighbor knew their own dog, and trusted that the neighbor knew their dog was great w/ all other dogs -- we probably would've introduced the dogs too. I put a huge amount of responsibility upon the neighbor for not knowing their dog....not good at all.
Maximo gave great advice about introducing dogs too. At the shelter where I volunteer, I'm approved to do dog-to-dog intros and we not only require a class to do it, but also 5 supervised intros before being approved -- and we have a very specific process for intros. Before doing intros at the shelter, I was way more lax about introducing my own dogs to other dogs, but not any more. So believe me, it is a learning process for sure....so again, don't beat yourself up so harshly; you don't deserve that
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So glad everything turned out okay in the end!