@Priya171 An unfortunate situation. I can fully understand not just being able to pick up and move with 2 kids in tow. Sometimes you just have to try to make the best of it.
It's sort of a chance one takes when booking a short term rental. It works the other way, too- hosts can end up with terrible guests who have misrepresented themselves and their intentions.
But for the most part, as you've found out, the majority of bookings go just fine from both sides. Sometimes it just doesn't.
One thing I can tell you is that posts on this forum seem to make it clear that guests often have bad experiences when renting places that are managed by these big companies. Many reports of poor cleaning and/or maintenance, poor responses from the "hosts", refusal to refund for legitimate issues, and bait and switch, which is what it sounds like you encountered- the place was not as pictured.
Listings run by the homeowners themselves, or a private co-host, that have good reviews, where they take personal pride in presenting a nice place and being responsive to issues and take reviews and ratings quite personally, are a better bet than these places run by companies with scores or hundreds of listings.
And while Airbnb can be quite punitive towards small time hosts when there are reports from guests, and issue refunds in many cases, they seem to ignore transgressions by these big companies, as they bring in so much revenue. They somehow get away with things the rest of us hosts can't.
If you want to be persistant and try to get some refund, I would do that on the basis that the amenities listed did not work, that it was misrepresented, and whatever else was wrong, rather than the fact that the host promised a refund he reneged on.