Shouldn't John hate Beth because she killed his wife / And why isn't Kasey traumatized about the incident?

Beth didn't kill her mother.

I still don't understand why they thought Beth killed her mom. I looked closely at that scene. Here's how it went down:
1. Evelyn tells Beth to open the gate. Beth's horse freaked out a little bit and bumped into Evelyn's horse, as Beth didn't know how to ride it properly ( because her parents didn't teach her or just ignored the fact that she's afraid of horses)
2. Evelyn's horse got on his back legs and then fell onto Evelyn.
3. Evelyn immediately blames Beth for this accident. Kacey offers to go get help, as he knows how to ride. Evelyn sais No, Beth did this, she should go.

So a grown woman, with an entire horse on top of her body, in need of immediate help, sends a panicked 12 year old, why cannot ride a horse, to get help.

To me this is on Evelyn.