What is the idea that Mrs. Sheridian does not want to put in Laura's head from "The Garden Party" by Katherine Mansfield?
This broken thought from Mrs. Sheridan is kept deliberately ambiguous by Katherine Mansfield. Most of the story is told from Laura's point of view; however, the reader gets occasional glimpses of what's going on in the head of some of the other characters, and occasionally a narrative voice intrudes which is ambiguous as to whose perspective is being relayed. The characterization of Mrs. Sheridan and the narrator's voice give us some clues as to what Mrs. Sheridan was about to say.
Mrs. Sheridan is first amused at Laura's reaction to the death of the neighbor, and then she loses patience. She tells Laura that "people like that" don't expect their upper class neighbors to sacrifice their pleasure for them. Once Mrs. Sheridan has enjoyed her delightful garden party, she finds it in her heart to send the leftovers to the "poor creature" who lost her husband. She loads the basket with enthusiasm and tells Laura to "run down just as you are." She starts to say, "Don't on any account," but doesn't finish the warning.
What might she have been about to tell Laura not to do? Earlier the narrator expounds upon the poor neighborhood down the hill from where the Sheridans live. The first part of this paragraph cannot be in Laura's point of view because it says things about the neighbors that Laura would not say from what we know of her early in the story. The paragraph states that the "little cottages... had no right to be in that neighbourhood at all." Then the paragraph describes how Laurie and Laura "were forbidden to set foot there." Readers assume that Mrs. Sheridan was the one who forbade them to go there, and the first part of this paragraph seems to reflect Mrs. Sheridan's viewpoint.
Now Mrs. Sheridan commands Laura to "run down" to the widow's home. It's likely that she was about to tell Laura, "Don't on any account go into her home." Mrs. Sheridan had wanted to protect her children from "the revolting language and ... what they might catch." Her views have probably not changed. She would want Laura to spend as little time as possible in contact with the lower class people and to not set foot inside the widow's home.
Laura herself says right away, "I don't want to come in." Yet she is whisked inside, much to her horror. It seems likely that Mrs. Sheridan was going to warn Laura not to go into the woman's house but decided to not even put such an idea into Laura's head.
This is a good question, unfortunately, there is not one clue in the text to tell us what Mrs. Sheridan was actually thinking. However, based upon what we do know of Mrs. Sheridan's attitude toward the people who live in the nearby lane, we can make a couple of conjectures as to what she might have been thinking that was best to keep to herself rather than put into Laura's head.
First, Mrs. Sheridan has no charitable feelings toward people in the lane and their houses since she restricted her children when they were from going down there because she was fearful of inferior and foul language and of diseases. Second, she believes that such people, whom she feels are inferior--as inferior as their houses--have no expectation that people of the Sheridan's class should or would make sacrifices for them.
From this we might conjecture that Mrs. Sheridan might be thinking, "don't on any account--invite the widow to call." She might be thinking, "don't on any account--talk to any young men in the lane." She might be thinking, "don't on any account--say you'll attend the funeral." She might be thinking, "don't on any account--say you'll go back to visit another day." With no clues of any sort, your guess is as good as mine. Frankly, I'm drawn toward "invite the widow to call," with "talk to any young men in the lane" a close second.