Rebuilding my entire Fallout Shelter

I made some construction choices at the start of my Fallout Shelter that I'm now unhappy with. Can I send 25 (the maximum) dwellers out to the wasteland and rebuild my shelter and have them come back to repopulate it?

I have maxed out my cash so I could make an amazing vault now...

TLDR: This is a bad idea

If you want to rebuild from the vault door, the only way is to remove all your living quarters and you can only do that if you first evict (or kill) all your dwellers. Including exploring dwellers.

Then you can rebuild. But, and here's the important thing. More dwellers don't just appear like they did when you started.

In theory this situation can be remedied by getting rare dwellers from lunchboxes. But I've opened 3 lunchboxes and no one has appeared...

Edit: After 4 weeks of nothing, I finally got someone from a lunchboxes. They operated the radio room until another came and now I have breeding stock. Game saved!

You cannot. Dwellers in the wasteland still requires living spaces in your shelter.

If you need to change the room directly connected to your vault gate, you must kill/remove everyone to be able to delete it.

Dwellers waiting at the vault door needs to be saved up so you can immediately put in new dwellers.

As Nelson said, just sending your dwellers out of the vault won't let you destroy all your rooms to rebuild.

What you can do, however, is rebuild step-by-step, or build some temporary accommodation out of the way somewhere (probably in a very deep level) then destroy all the other rooms and rebuild. I've done this a couple of times. If you're planning on moving your lift shafts around it can be a faff, but it's eminently possible.