@Joe2662 This sounds like a somewhat inexperienced host? A host can't simply cancel a guest reservation without penalties which are quite extensive and it seems she wasn't aware of that when trying to cancel your booking. The host would get a $50-$100 fine, the dates she cancelled would be blocked by Airbnb so she, in fact, would not be able to rebook them, a notice would appear on her review page saying "Host cancelled this booking", which makes future guests wary of booking with her, and she would be ineligible to acheive Superhost status for a year, or lose it if she was already a Superhost.
If the place wasn't a good fit as far as you were concerned, it is up to you to cancel. The host can authorize a full refund or partial, as she sees fit.
If it not being a good fit was mutual, then you should have called Airbnb to explain this, and they would do a "neutral" cancellation, where you get refunded and the host isn't penalized.
Also, if you guys were trying to do all this on the app, the desktop version has functionalities that the app doesn't. If something isn't working correctly, you should try on a laptop.
I can't advise as far as altering booking dates, as I've never had to do that.
Guest payments are charged when a guest books and the funds are only released to the host 24 hours after the guest checks in, and it can be up to a week after that before the money appears in the host's bank account. So that you were charged and the host hadn't been paid yet is normal. For that reason, it's not really fair for a guest to expect a host to refund them immediately if they cancel, even if the host is amenable to refunding. You can't refund money you haven't received yet.
Was this place not a good fit because you weren't clear on what you had booked, or because the host's listing wasn't clear as to what she was offering? Just curious.