I'm guessing you've used all of them, but here are the "arguments" you could use with the custodial parent:
1) Ask why (what data) she has that the general ed material is "too hard?" Has the child verbalized this? Are grades falling? Does she struggle doing homework with her?
2) Explain that is wouldn't be fair to the younger child to stay on the same track as the older child if the younger child is more capable - could lead to resentment later on.
3) Is the grandmother able and willing to engaged the younger child in social activities that help with the socialization of home-schooled children? Or will social skills and interaction suffer?
4) Would she be willing to try the gen ed setting for a while with supports to see how the child does before pulling him/her to home-schooling? Gather more data? Speak with the child after each school day for indications of struggles? Check in with the gen ed teacher?
I don't know much about home-schooling, but I would guess if the grandmother uses a state-approved program there would be no educational neglect.