We can get AssetUrlSelector to work on the site collection it is placed in. But how can we get it to use another site collection?
This control is not designed to browse for items in another site collection. This is apparent from its decompiled code and also the wording on its MSDN article.
About the closest you can get is the
AllowExternalUrls property which at least allows users to copy and paste in a URL from another site collection.
You can define all the external site collections by going to the Site Settings -> Suggested Content Browser Locations. After that when you open up an AssetPicker, look on the upper left of the Modal Dialog. Look for the Suggested Location drop down. Here you can select the site collection you have defined previously. Read more here http://blog.mastykarz.nl/easier-working-assets-cross-site-publishing/
Hope this helps