Indeed a powered off disk can bear more stress than an active one. When reading/writing the heads are 'flying' at a few micrometers distance of the platters. If by a bump the heads touches the surface of the platter, you'll at least loose some sectors, but probably the whole disk.
But if the disk is powered off, the heads are parked on a safe place, where they can't hit the platters. On the other hand, it's still a precision device, and if you drop a disk from one meter on a hard surface, it's almost sure broken.
Actually I was more concerned about the connectors. The (sata and power) connectors are inserted in a slot on a pcb. In most cases the disk is fixed on a cradle, which is shoven in the nas. This construction is just not intended to be moved a lot. A bump will break the connectors.
A disk which is constructed to be moved, like an USB disk, has the disk fixed on the same frame as the connectors slots, so that the connectors won't be loaded extra on a bump.
Are there no 3.5" HDD's that have similar features as the 2.5" HDD's in laptops.
No. The reason that 2.5" disks are stronger, is because they are lighter, and so the forces are just smaller.
In your case I think I would put a NAS on both places, and let them sync each other over the internet. It's the golden rule for backups. Make sure that you have 2 different copies on 2 different places. Well, those places doesn't need to be a thousand kilometres apart. but it won't hurt either.
I must admit that I have no experience in doing so using the stock firmware. I have two NASses on different places which sync each other over an ssh tunnel. On one side I have no access to the nat router, so that end connects to the other, and I don't care about ports. I only need one, and it doesn't matter which.
You can have a look at btsync
. It will run on about any nas on which you can install custom software. It will sync transparently, you can also run it on your PC/laptop, if you like, and it doesn't care about ports. It uses Voodoo to find each other.
I did some tests with it. Both were behind a nat router without any port forwarding. They found each other in 10 seconds, and synced straight away.