[There's a long pause as she considers if there's a permanent cure to homesickness, without visiting home.]

Please don't think of it like that. Even if it's only for a short time, those moments without it will feel wonderful. [...Oh, maybe this would work?] The battle dome can create any sort of environment you know. Perhaps you could recreate your home in a simulation? It won't be the same as being there, but it would be close.