@agilefeet The fact is, the dog tried to bite the baby. Therefore: dog is not safe for baby; baby is not safe around the dog. This is very, very, very simple math. Dog + baby = unsafe. Your job as a parent is to keep baby safe.
I get the sense that there is awkwardness or tension because someone is trying to negotiate the facts here and convince you your math is wrong, when everyone knows there’s only one possible outcome of this event: the dog is no longer around the baby.
You’re not passing judgement on these people or their dog by just stating the facts, and you don’t need to apologize for keeping your baby safe. So just be matter of fact when talking about your plans.
“We obviously won’t be able to stay with X because the dog is not safe for the baby.”
If the gathering is at someone else’s house: “The dog needs to be put away/ not be there when we come over because the baby is not safe around the dog. Is that something you can guarantee, or should we plan to visit at a different time?”
If the gathering is at the dog owner’s house: “We won’t be able to come unless you’re able to put the dog away when the baby is there. If that’s a problem, please let us know so we can cancel our plans.”
Some other lines you might need to break out:
“I understand the dog has been great around other kids. That’s not been our experience, so we’re not willing to risk it.”
Any mention of the word overreaction: “I understand your desire to downplay the situation, but the fact is that the dog bit our baby. We got extremely lucky last time, and we’re not likely to be that lucky again. You may think the risk is small, but it’s not one we’re willing to take.”