"I am walking through your house."
Translation:Idę przez wasz dom.
"Idę przez twój dom" =I am walking through your house.
Za pośrednictwem means with intermediation , it translates to through when a third party hepls you do something.
I am walking past your house , and I am walking by your house both mean Idę obok/koło twojego domu.
I am walking to your house = Idę do twojego domu.
( You do not skip "twojego in sentences like those. If you skip it is assumed the house is the subject's own )
Also You should say , that your beautiful wife is "Polką", as we do not use adjectives to inform about nationality.
After przez you always need accusative. Dom is masculine not animated so it has Accusative=Nominative.
In Accusative of masculine nouns, it matters whether the noun is animate or inanimate. If it's animate, the form is identical to Genitive. If it's inanimate, the form is identical to Nominative.
A house is inanimate, so the Accusative of "your house" is the same as the Nominative: "twój dom".