In the example sentence
私の家をあなたの家のように扱ってほしい。
translated as
I want you to treat my house like it’s your house.
Is the implication that I want the listener to take very good care of my house? Or that they should make themselves comfortable, and act as though they are in their own home?
Well this is a cultural thing. In general a Japanese person would never let themselves be invited to a house they would not respect. Though I cannot say everyone is so steadfast as to never be impolite.
The idea that a person could say a phrase that would give you permission to go counter to your cultural upbringing is hard to imagine.
As a Japanese person, if some one says this to me, I would think, ‘Oh shoot, what did I do wrong?’ To me this has the nuance of, ‘Please, I want you to treat my house like how you would want your house to be treated by guests.’ I think I get this vibe from this sentence because of the word 扱う, since that word means to handle or to take care of. The use of that word makes it sounds like they are prioritizing the house and not you, if that makes sense.
Personally, I would never use this sentence for hospitality purposes since the person I’m saying this to might assume that they did something wrong. I would probably say something like, 気楽にしてね, or be more direct and say, 遠慮しないで、勝手に冷蔵庫のものとか食べたり飲んだりしてもいいからね。
Many thanks!
From my limited experience it seems like it’s always better to be very specific and straightforward with Japanese, since may things are left to “read the air”, being explicit in my intentions usually helps being understood.