Well it sounds like for the most part you already know what it means but I'll give it a whirl and maybe it'll help you discover something new.
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I dreamt I was sitting in my living room with my cat, watching TV
These things are comforting. They represent things like security, stability, peace of mind.
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when suddenly an ambulance comes plowing through my backyard and into the house. I and my cat got out of the way in time, but in my dream, the ambulance plowed through the back wall thereby destroying my TV and its stand, into the couch, and came to rest *in* the weight-bearing wall in the center of the house (my house has few interior walls, but those that are there hold up the roof).
An ambulance represents a state of emergency, a need for urgent care, something that needs attending to that is very important. The fact it plowed through your house and ruined your sense of security and peace of mind indicates this is something important that is bothering you in a profound, or at least abrupt way.
An ambulance can also indicate emotional issues. The severity of which only you would really know. It might be major, maybe not - most likely somewhere imbetween.
You mentioned a desert landscape outside your house. Deserts represent isolation, loneliness. The most logical answer to the over all meaning of the dream is that pressumably you feel lonely or isolated from your peers (perhaps you are missing that special someone, or never found them, maybe you're not as well liked as you wish you could be, maybe your family has been distant) and its affecting your personal sense of security, maybe your self esteem too. But I think the desert actually represents introspection. Its not that you are isolated from the world, but that the issue of what ever the ambulance represents is affecting only you and only you can figure out what it is.
In away you dream could be interpreted as a premonition. That something big and disturbing will happen in an abrupt way. But because you know an ambulance can't ruin your house in real life - the house in this case is you as a whole - means that what ever may come won't be the end of the world or nothing you can't deal with.
As much as you look towards the future I would advise not to try to change it because you may only cause the future to happen the way it was meant to, or worse you could make the situation worse. Also as much as you look outward for answers realize the majority of them are within you already. I think introspection would be good for you. And if you are isolated and lonely I'd follow Valkyries advice.