Shared storage between VMs

Solution 1:

SHort answer is yes, but you'll need to use a cluster filesystem (e.g. GFS2) on the shared drive to avoid conflicts - IMHO it would make more sense to use the vm host to export the large drive as a network filesystem (NFS or SMB) and mount it on the VM clients.

another intention is for all VMs in each box to back up to the other server box. E.g. VM1 and VM2 on box 1 will back up their data to box2 and VM3 and VM 4 on box 2 will back up their data to box 1.

You've not said what operating systems are in the mix here. Rather than 'back-up' the VMs, it may make more sense to make the storage available independently of the host and use asynchronous replication via replicated filesystem (e.g. AFS, DRBD) of the underlying substrate.

Solution 2:

Yes. Install visualization of the some kind on both machines. On the machine with the drives, install a SAN VM, provide iSCSI/NFSv3/4 or SMB3+ storage to the hypervisors (each can accept own file protocol, all of them can do iSCSI), all other VMs run off that shared storage. This isn't production setup as shared storage is SPOF (Single Point of Failure), but lab use is definitely OK.