ho= be ghar=home chahe=wish chahe ghar ho ya taare ya registan--- if you wish it be a home ,stare or desert

“हां,” मैंने कहा, “चाहें घर हो, या तारे या रेगिस्तान उनके सौन्दर्य का कारण एक अदृश्य होता है।” it should not be चाहें, it should be चाहे* without nasal dot. May be a typo. With this correction in place the sentence mean. "Yes," I said, "whether its home, or stars or desert, reason of their beauty is invisible" "चाहें घर" is not correct breakdown while interpreting the sentence. The sentence structure is equivalent to English "whether ... or ..." चाहे ये या वो "Whether this or that ..."

you are correct here but the feelings of "chahe" is not included in your sentence again " I told to little prince ,as per your wish, it may be a home , stars or desert but the cause of their beauty is an invisible thing."