Hmm, well... I mean, I'm sure you're not completely alone, haha. But for me, I don't know... I feel like, when dealing with a fictional TV show, some things have to be taken on faith, as part of the premise. This isn't real life, just a story, and also different people just... react to different things differently. So. In the show, it was made fairly clear that Lorelai and Rory were happy there. They have fond memories of the place. Rory is eager to show her grandmother the place she sees as her first "home," and doesn't anticipate Emily's negative reaction to it. They made it cozy and homey. And, I mean, yeah, an uninsulated potting shed is not an ideal living situation in real life, especially for a very young child, but... humans throughout most of history have lived in largely uninsulated structures. As the characters were presented on the show (which is really all that they ARE, given that they're fictional constructs), Mia was a kind woman, so I can't see her letting them freeze to death or whatever. I'm sure she would have made arrangements for their safety if needed. The Inn, with plenty of heat and a fully-staffed kitchen, was just a few meters away if they ever needed to have "sleepovers" there on especially cold nights. I don't think there's a "hidden dark side" to Mia, who, as a fictional character, does not exist outside of what was written for her.
Should Mia have offered to let them live with her, in her actual home? I don't know. Maybe she didn't have room. Or maybe... Lorelai wouldn't have accepted that. She ran away because she wanted to make her own decisions for herself and for her daughter. Having her own "place" was important to her. Should Mia have paid for an additional actual apartment for them? I don't know if she would have been able to afford to pay rent for a second apartment in addition to her own housing expenses for ten years. There's no indication that Mia was a wealthy woman, and that's a substantial expense for most people. Lorelai and Rory living anywhere else would require them to pay rent. That's just how the world works, unfortunately. So, Mia let them live in a building that was already on her property, made it as comfortable as possible, and yeah, let them stay there for free. I don't know, I think that's still pretty nice. Lorelai not having to pay rent (which she would have had to do anywhere else) for ten years is the thing that allowed her to save enough money to BUY A HOUSE as a single mother in her twenties. I'm pretty sure Lorelai and Rory would have still been stuck in a crappy apartment otherwise (maybe upgrade to a slightly nicer apartment? But still an apartment nonetheless).
