@Ian27202 Thanks for explaining further. I mistakenly thought you were wanting a refund for the whole stay, rather than just getting your double payment for the one night back. Sorry.
You really should be honest in your review about the conditions, otherwise other guests will just have to face the same bad conditions. I can see you felt kind of sorry for her, you sound like a kind person, but hosting is a job, like other jobs- if you don't attend to important parts of your job, you won't have a job anymore. That's how the world works. When bad hosts are just allowed to continue to not repair things and give guests a bad experience, it gives Airbnb and other hosts, by extension, a bad name. A review which mentions what wasn't working won't get her delisted, but it might make her realize that she needs to be more responsible. And really, in my opinion, a host who cheats a guest like this should be delisted. She'll just have to find another way to make money.
I was a poor single mom, too, many years ago, with 3 kids. But that's not an excuse to rent out something that's not decent. If she can't afford to fix things which are essential, like a toilet, then she shouldn't be hosting, and if she can't afford to fix things that aren't essential, she shouldn't tell guests she has those things. It sounds more like she just doesn't care.
You don't have to be mean about it, but you should state in the review the things that needed dealing with. There's nothing wrong with not providing a TV for guests, for instance - I don't have a TV in my house at all, but then she needs to remove the TV from her list of amenities. Hosts shouldn't tell guests they'll have this or that if those things don't work properly.
If there are messages from the host saying she'll pay you back, then I agree that Airbnb should deduct what she wrongly took from you from her next payouts, and refund you that, but they don't like hearing that cash was exchanged- it's against their policies, so they are just washing their hands of it all. You could try being persistent, but I think it will be a waste of your time. I don't know know how much money you're talking about here- you have to decide if it's worth hours of your time to pursue it. It's terrible of her to have cheated you like this, but I think it's just one of those things you're going to have to let go. Consider it an involuntary donation to a poor, dishonest, single mom, if that makes it any easier to stomach.
And if a place only had one review that only said it was "okay", I'd take that as a "not okay". If a place is good (doesn't have to be fancy, just clean and everything in working order), and the host behaves responsibly, a guest usually has more to say about it than that. That guest maybe felt like you- thought the place was pretty bad, but didn't want to hurt her with complaints or cancelling and leaving.