You could recreate the control in some way with two decks. The first deck would be all your child options, and the second deck would be the junction object records (between the parent and child). Action on the cards in the first deck would create a record in the junction object and prepoluate the child ID from the card's context, and the parent ID from the page context. (You wouldn't need arrows). Other posts here have described drag and drop ordering.
But there are other ways of allowing this sort of selection. Some ideas:
Build a "tagging interface" that shows the junction object records as buttons. Adding a new tag can be done with a picklist interface.
Use a table of child records - and add a row action to the table that creates the junction object record.