It sounds to me the real problem is you are positing informaiton/opinions/conversations on FB that should be personal and could at the least be misundertood if not clearly offensive. You didn't tell us what you actually wrote, but if it is something like "so and so would be offended if we didn't visit..." Well that is obnoxious and I think you shouldn't have said it and apologized. I woudl be offended by that if I was the aunt.
For the issue of getting to know them and visiting... Your husband has been estranged from them, and as the child in the situation, I think they as his elders have more obligation to make an effort to get to know him (i.e., visit you or sending a very clear invitation). He certainly can reach out if he wants, but I could understand his reservations.
However, I might try to put yourself in their shoes a little as his extended family. I don't think it was right to stay out of your husband's life. But they are in a tough spot if your husband's parents don't have a good relaitonship wiht him. Perhaps they were just trying to stay out of it?
That said, if they have expressed an interest in getting to know you all and your husband wants this for himself and his child, then yes, I think you should also make more of an effort to see them. Right now, it sounds like their feelings are hurt because you were basically talking about them out of school, and I think you probably should make a good faith gesture.
How to fix this? Write a poilte and personal note saying that you apologize for discussing his family online and you are still getting used to the complicated relationships in your husband's family. Simple, leave it at that. Then say, we woudl love to get together and have you meet our son. Becasue of our car problems, we won't be able to visit until the spring, but would you like to come see us before then? Maybe after the new year?
As for Christmas, however, I don't htink you need ot offer 100 excuses. You didn't get an invitation and already have plans. Tell them "Merry Christmas" and try to arrange something for another time.