Putting down the dog is old business, and because the dog lived in HER house, you don't have a lot of leeway in it.

The snakes live in your house. If she starts in about the snakes, then say "I'm sorry, but I don't want to discuss with you, unless you will be reasonable". If she won't, then change the subject and refuse to speak about snakes.
If she's on the phone say "I have to go." and hang up. Every time she starts ranting about snakes, turn and leave, politely, or hang up after a polite goodbye.
If every time she becomes unreasonable, you leave, she has no one to argue with, you are not having any screaming matches, and at WORST, you'll not have to listen to orders to get rid of your pets. At BEST, she might start to be more reasonable, bit by bit. At any rate, it will stop the ranting and demands, without any fighting.

It's your life, and you have to stand up and refuse to fight, or in your case, cringe because "mom" doesn't approve of part of YOUR choices. It shouldn't matter that she doesn't approve of every choice you're making. She won't approve of other choices you make later, it's part of being an individual.