I see in the loading tips it says you can open the vault door, but it doesn't say how, any help?

By sending out dwellers, or letting them in. It'll open because dwellers cannot walk through walls. They need doors or open space, unlike multidimensional beings.

I was under the assumption that you could leave them in an open state....how does sending the dwellers to their doom in the wasteland make them happy?

Oh but they might not necessarily be happy about it, but you should Dwellers in the wasteland gather weapons and outfits to help the dwellers inside the vault and out.. It's a beautiful cycle

Recently i've experienced really funny thing. I was completing the "send xx dwellers in the wastelant" task and Deathclaws attacked when one of my dwellers just got out. They waited for him to get out and for the doors to close. Really well-behaved creatures

... and intelligent also, since you usually send your best geared dwellers to the wastes.

Seems that the Vault is a Super-Duper Mart full of canned meat for them.

Nah, i have three high level dwellers in luck training room and one high level dweller in storage room on top floor, they have my second best weapons (two of my best weapons are always free to deal with incidents or to be switched in case of DC attacks) and they rarely make it to the second floor. If they were so smart, they would never come again