Finding polygon neighbors within a distance but excluding polygons with same hhid

[Ritikakhurana]

There are two datasets I am working with. 1). A survey dataset that has a household ID and property IDs. The survey dataset is such that a household can have more than 1 property.  5). Publicly available property dataset of the entire area that I have survey dataset of. This means that are some overlaps in the two datasets. 

Now, I want to identify neighbors of each property but exclude properties that have the same household ID. Along with this, I want to constrain the identification of properties by distance. 

Please see screenshots of my dataset below. In the photo below, orange lines are survey data properties and black polygons are public dataset. 

I tried buffer analysis but only creates a circle around one property but doesn't exclude properties of the same household.

I cannot work with Polygon Neighbors because that is not consistent with my economic theory. I need to include neighbors that do not share same boundary. 

Can someone please suggest to me the right tool? or explain me how to use model builder for this case?

Thanks!