The most important thing to know about creating Panel, Gizmo, JRemote, etc. Views is that you must close MC and restart it in order to see any changes to the View on the target device.
Even then, MC will cache the contents and level naming of the Views, and it can take a while, and a bit of clicking around, to see the changes come through.
You can't use the "Playlists" menu type because, as you found, it isn't configurable and can't be nested. You can, however, create a top-level item and give it your daughter's name, then add levels below that as required. Use the [Playlists] pseudo field to add your daughter's Playlists to the top-level item, or more correctly limit the contents of the top-level item and all level below to only your daughter's Playlists, using the "Set rules for file display" rule "Playlists... is any..." then select all her Playlists. That means there is a bit of maintenance involved, but there isn't any function to set a rule of say "Playlists... contain... Cindy", as an example. That is because the [Playlists] pseudo field function actually is interpreted as "playlistid==724062238,=11407219". i.e. It allows you to select specific Playlists.
I set up a top-level item called Cindy and limited it to some sample Playlists I use for testing, "One Track", "One Album", "Two Tracks, "Two Albums", "Three Tracks", and "Three Albums". Then I set up Library Items below that called "One's", "Two's", and "Three's". Inside each group I selected the matching Playlists using the [Playlists] pseudo field again. That works, but it shows all Tracks within the Library Items lumped together, rather than showing the individual Playlists to drill down further into.
I could have selected a Playlist Group as a Category in a Library Item... or should be able to. But perhaps as you found, that doesn't seem to be working. That appears to be broken.
You can also select a Playlist Group using the "Playlists... is any..." rule, but that also lumps all the files together in the one group, rather than showing the Playlists within the Group.
So basically it looks like with the current functionality you need to set up a Library Item for each Playlist, if you wish to keep them separate.
Anyway, does that give you a start? Restart MC after any View change. Refresh, refresh, refresh. There are lots
The functionality is pretty thin for Playlists management in Views though. It could be better. Even the Theatre View functionality would be an improvement, but that could be better as well. Just being able to set a rule of "Playlists contains Cindy" would be an improvement everywhere.