Your hierarchy is Groups -> Items. I'm assuming the user must select or create a group before dealing with items. So you probably want to start with the list of groups in a panel on the left side.
Creating/editing a group can either be done within that panel or within a popup/lightbox.
To the right of the groups, you can list the items in the given group. Think of an email application where you select a thread (group) on the left, and see the messages (items) on the right: http://designinginterfaces.com/patterns/two-panel-selector/
Now for the filtered list adding: Instead of having the user "add an item to a group," could you consider having them "select the items" from the list that they want to be associated with the group? Think of the groups as labels applied to a master list of items.
By default, the list of items could be filtered to show only those that are selected for the given group. The user can expand these results by activating one of the other filters, like produce, thereby showing all the produce items, selected or not. The user can see which produce items are already selected, and turn each one of them "on or off".
With this model, you'd always want to display the total number of selected items for the given group, and have a quick link to get back to the default view to only show selected items.