Gmail – How to jump directly to a Gmail label in “Move to”

select the label, in the search bar, it will show label:mylabel - add label:unread and search.

select all messages by ticking the top left checkbox

if there are more unread messages than can be displayed, a small notice will appear above the first message in the search results - you want to select all messages which match the search.

now you can click the 'more' button and select the 'mark as read' option.

As an alternative, have you tried the Multiple Inboxes lab feature?

Click the gear icon -> Settings -> Labs, and find Multiple Inboxes. When you have activated it, a new tab appears on the settings screen.

It lets you divide your inbox view into multiple sections. Each section displays the results of a pre-defined search.

It should be possible to specify a search that includes your label and its sub-labels, but you would have to update the search term if you add new sub-labels.