"As the apostle Peter said to Jesus,... 'Lord, where will we go away to?' This is Jehovah's organization ..."
No. You probably know this, but compare how your mom misquoted this verse to the actual wording from the NWT:
Simon Peter answered him: “Lord, whom shall we go away to? - John 6:68
This is an extremely common misquotation by JWs. The change may be subtle, but the implications are profound.
Notice that Peter actually said "whom" not "where."
This slight change in wording shifts the focus from Jesus--which is where the Bible writer wanted it--to the WTBTs, which is where they want it.
One word change and it's no longer about Jesus but about the organization. The confusion in your mother's mind is obvious as she follows up her WT worded misquote with the WT indoctrinated belief, " This is Jehovah's organization ..."
And thus are the minds of the unsuspecting easily misled and manipulated.
Remember, your mother is in a high-control, manipulative cult. She is no doubt completely unaware of the devices and techniques which have been used on her for 55 years to so completely indoctrinate and control her.