spoilers for episode 4

Skreamzu said:
He didn't want the alliance with humans and therefore wanted to trick his father into thinking the humans killed her, so the father holds a grudge against humans and stop the alliance.
(at least that's what I understood, correct me if I'm wrong)

Lelouch12cc said:
one reason was that he wanted his father to turn against the humans for killing his wife , the second more profound reason was that as Lord Godard mentioned that the family was running on the ideals of his late wife , so roul killed his mother , because he didn't like her idealism of human and monster friendship
plus his wife was a former human so maybe thats also the case , but most probably it's because he hated how she encouraged Lord godard to become friends with human

ShaggyBoyy said:
can anyone explain why Raoul killed her mother? I understood that he made it look like a human killed the mom and all the other stuff. 
I heard it mention that Raoul killed her mother because they were allied with humans and he thinks that hes superior because hes a vampire. But why was the mother killed? I may have been missing out on something.
Tysm in advance