Right now you have no credit. If you buy a house, it sounds like you won't be able to make the mortgage payments. Which will result in a foreclosure and killing your credit. So I really don't think that buying a house is in your best interest. Your landlord sounds like he's being unfair, possibly. When you signed the lease, did it specify if you can have pets? If you're allowed pets, then he can't evict you for having dogs. The most he would be able to do is keep your security deposit when your lease is up. Saying he had to pay to have the place cleaned because of the dogs.
I would try to talk to him and be both mature and polite. Ask him what you can do to ease his worries about the dogs. And if you owe rent, show him that you're working hard and have a plan to pay him back. That may mean finding an additional job for a bit until you get back on your feet. Or if you can't pay the rent, it sounds like you may need to find a place with a cheaper rent until you guys move somewhere new.
You have to think of your future here and buying a place does not sound like it's in your best interest. Sounds like you'll ruin your credit. I would do what you can to stay where you are for now. Then when you're financially able, you can invest in your own home. Owning means they won't evict you, the bank will foreclose on your home instead.
You may have to find a new home for your dogs. I'm a huge animal lover and I know how sad that thought is for you. But right now, you need somewhere to live. Maybe you have a friend or family member that would keep them until you move? That sounds like the best option. Then you can take them back when you're moving somewhere new.
Sorry you've hit such a rough patch and I wish you the best luck. :)
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kid, I wrote back,
all lovers betray.