TanyaYatskovska , I met the same issue.
Below is the script, it's written in VB
Dim LibraryCollection
set LibraryCollection=Aliases.Inventor.AInventor.Pane_AssetBrowser.tvw_Asset.WPFObject("TreeViewItem", "", 3)
Call Aliases.Inventor.AInventor.Pane_AssetBrowser.tvw_Asset.ExpandItem("|[2]") 'expand project library node
Dim TargetAsset
set TargetAsset=LibraryCollection.WPFObject("TreeViewItem", "", 1).WPFObject("TreeNodeBorder")
Call TargetAsset.ClickR(55,5)
TargetAsset.PopupMenu.Click("[4]") 'right click the target asset and edit
delay(20000)
Common_Routines_Factory.RefreshNamemapping
While Aliases.Inventor.AInventor.Pane_ModelBrowser.zcrumbCtrl_ModelBrowser.ChildCount(4) <> "Ready"
aqUtils.Delay 2000
statusBarObj.Refresh
Wend
call Aliases.Inventor.AInventor.Pane_ModelBrowser.Click(70,35) 'switch to Asset builder sub page
and after seeing your solotion provided, I tried adding "delay(20000)", and refreshnamemapping "Common_Routines_Factory.RefreshNamemapping", but they don't work for me.
and for this mapped object Aliases.Inventor.AInventor.Pane_ModelBrowser.zcrumbCtrl_ModelBrowser do has the property childcount, you could check it from the screenshot.