I use a Microvault from Gunvault. I don't know if it can be mounted under the seat. It does have mounting holes in the botom Depends on the vehicle I guess. I also use it as a locking case when flying.
That will work. It is not meant to be long term storage, I would only leave my gun in their while I'm busy in the gun free zone. I do however unload my gun before storing so if they do get the gun they'll have to have better luck than me at finding ammo. Some even remove the slide before storing.