Although rare there are courtyard villas that meet your needs. I have a courtyard villa that is on the edge of the development, so I have a wall, not a neighbor's house, on the other side of my back yard. Courtyard villas have outside walls (7+ feet high) and solid fences (similarly high) that separate one neighbor from another. The size of the backyard for courtyard villas varies; I have room for a pool but the size may or may not be enough for your dogs.
Because I have no neighbor next to my yard nobody needs access to my yard. However, if I want access to the side of my house that is effectively the wall for my neighbor, for example, to power wash my house, I'd need to let them know. As noted above, the property line runs roughly between the houses; the sideyard easement referred to above is an easement that allows my neighbor on that side of the property to modify and maintain everything up to but not including the wall of my house.
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