Redesigning this interaction will of course require some reconsideration from your side, which I acknowledge can take time to think through and get right.
Until, that (eventually) comes you can however without much difficulties get the parents of the all these dialogs in place.
If you like I work with two screens and have the Vault GUI client open on the secondary screen you will see:
- Main window on screen 2
- First level unshelve dialog on screen 1
- Second level unshelve dialog on screen 2
- First third level unshelve dialog on screen 1
- Second third level unshelve dialog on screen 2