Mrs Alexander knew about Christopher's mother's affair, but not about her 'death'.
In the same conversation when she tells Christopher about the affair, he tells her that his mother died. She was shocked to hear this, but she took Christopher's word for it. Perhaps she'd known her neighbours well enough to know about the affair (or perhaps she'd heard about that through gossip from other neighbours who knew them better), but she probably assumed that Christopher's mother had gone away with Mr Shears and she simply hadn't heard about her death. Perhaps the affair was common knowledge in the neighbourhood, and Mrs Alexander assumed that the death was something less talked about (scandal always makes for better gossip than tragedy).
After all, if the lie about Christopher's mother's death was good enough to fool Christopher himself - her own son, and a boy with a shrewd and enquiring mind - surely it can't have been something that a neighbour who didn't know the family very well could have seen through.
Then she sucked in another big breath and said, “Because... because I think you know why your father doesn’t like Mr. Shears very much.”
Then I asked, “Did Mr. Shears kill Mother?”
And Mrs. Alexander said, “Kill her?”
And I said, “Yes. Did he kill Mother?”
And Mrs. Alexander said, “No. No. Of course he didn’t kill your mother.”
And I said, “But did he give her stress so that she died of a heart attack?”
And Mrs. Alexander said, “I honestly don’t know what you’re talking about, Christopher.”
And I said, “Or did he hurt her so that she had to go into hospital?”
And Mrs. Alexander said, “Did she have to go into hospital?”
And I said, “Yes. And it wasn’t very serious at first, but she had a heart attack when she was in hospital.”
And Mrs. Alexander said, “Oh my goodness.”
I said, “And she died.”
And Mrs. Alexander said “Oh my goodness” again, and then she said, “Oh, Christopher, I am so, so sorry. I never realized.”
Then I asked her, “Why did you say ‘I think you know why your father doesn’t like Mr. Shears very much’?”
Mrs. Alexander put her hand over her mouth and said, “Oh dear, dear, dear.” But she didn’t answer my question.
So I asked her the same question again, because in a murder mystery novel when someone doesn’t want to answer a question it is because they are trying to keep a secret or trying to stop someone from getting into trouble, which means that the answers to those questions are the most important answers of all, and that is why the detective has to put that person under pressure.
But Mrs. Alexander still didn’t answer. Instead she asked me a question. She said, “So you don’t know?”
And I said, “Don’t know what?”
And she said, “I shouldn’t have said what I said. And if I don’t explain, you’ll carry on wondering what I meant. And you might ask your father. And I don’t want you to do that because I don’t want you to upset him. So I’m going to explain why I said what I said. But before I do that you have to promise not to tell anyone I said this to you.”
I asked, “Why?”
And she said, “Christopher, please, just trust me.”
And I said, “I promise.” Because if Mrs. Alexander told me who killed Wellington, or she told me that Mr. Shears had really killed Mother, I could still go to the police and tell them because you are allowed to break a promise if someone has committed a crime and you know about it.
And Mrs. Alexander said, “Your mother, before she died, was very good friends with Mr. Shears.”
And I said, “I know.”
And she said, “No, Christopher. I’m not sure that you do. I mean that they were very good friends. Very, very good friends.”
I thought about this for a while and said, “Do you mean that they were doing sex?”
And Mrs. Alexander said, “Yes, Christopher. That is what I mean.”
-- Chapter '97' (emphasis mine)