Help make sense of this Duolingo sentence?

Lorena le dice a su esposo: "Creo que nos odiamos con los vecinos. Él nunca me habla y ella siempre te mira mal."

So, I understand the meaning here to be "I think the neighbours hate us," but I am confused about the grammar. Literally, it seems to say "I think we hate each other with the neighbours," which doesn't quite make sense. Why is "con" used with odiar in this example? I haven't seen that before.

'Odiar' is being conjugated in the first person plural, but does that include only Lorena y su esposo, o los vecinos también? If the neighbours are included in that first person plural, then does it actually translate to mean: "I think we and the neighbours hate each other"?

Is the original sentence in bold any different from saying "Creo que nos odian los vecinos." ?

submitted by /u/trampled_rose77
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