자식노드들이 뜰린다는 말이 무슨 의민지는 모르겠지만 다음과 같이 햅세요.

TreeView의 OnDragOver 이벤트

procedure TMainForm.TreeClientDragOver(Sender, Source: TObject; X,
  Y: Integer; State: TDragState; var Accept: Boolean);
begin
    Accept := True;
end;

그리고 onDragDrop 이벤트에서
procedure TMainForm.TreeClientDragDrop(Sender, Source: TObject; X,
  Y: Integer);
var
  tmpNode : TTreenode;
  AttachMode: TNodeAttachMode;
  HT: THitTests;
begin
    if TreeClient.Selected = nil then Exit;
    if TreeClient.Selected.Level = 0 then begin
        MessageBox(Application.Handle, PChar('최상위 노드는 이동할 수 없습니다.'), PChar(App_Title), MB_OK+MB_ICONWARNING+MB_TOPMOST);
        Exit;
    end;

    tmpNode := TreeClient.GetNodeAt(x,y);
    if tmpNode <> nil then begin
        if (tmpNode.ImageIndex <> 0) and (tmpNode.ImageIndex <> 1) and
           (tmpNode.ImageIndex <> 2) then
            Exit;
        if (ParentImageIndex(tmpNode) = 1) and
           (ParentImageIndex(TreeClient.Selected) = 0) then begin
            if MessageBox(Application.Handle, PChar(FmtMessage('임시그룹으로 이동시 해당 그룹(사용자)를 더이상 모니터링 할 수 없습니다.%n이동하시겠습니까?')), PChar(App_Title), MB_YESNO+MB_ICONWARNING+MB_TOPMOST) = IDNO then
                Exit;
        end;
    end
    else
        Exit;

    HT := TreeClient.GetHitTestInfoAt(X, Y);
    if (HT - [htOnItem, htOnIcon, htNowhere, htOnIndent] <> HT) then
    begin
      if (htOnItem in HT) or (htOnIcon in HT) then
          AttachMode := naAddChild
      else if htNowhere in HT then
          AttachMode := naAdd
      else if htOnIndent in HT then
          AttachMode := naInsert;
      TreeClient.Selected.MoveTo(tmpNode, AttachMode);
    end;
end;