Can a landlord demand that I get rid of dogs 2 years after I have lived there? There is no damage caused by them. She said she was going to tear down the fence and other things while I still live there

Do you have a written lease ? Is there a specific clause about the animals.

If month to month lease, how much notice are they giving for it

Yes she can, unless you have something in writing allowing them. And she can tear down the fence, and any other changes to the grounds, or even the interior with notice. Your best bet is to politely ask for time to find a new place to live, perhaps 9/30, with all sorts of promises about paying until the end and doing a super cleaning. Negotiation is key.

Unless you have a lease either stating that pets were allowed or not stating that they weren't then you are a month to month tenant. The landlord can then give you 30 days notice for almost anything.