File Sharing using Hyper-V Shared VHDX
Solution 1:
Yes. You can not share a file system between mupltiple computers UNLESS THE FILE SYSTEM IS EXPLICITLY DESIGNED TO DO THAT. Because computers cache the meta information and assume they are the owner.
Solution 2:
Shared VHDX is block sharing, not file sharing.
Now for a little digression in terms, since you're far from the first person to ask this question. A disk is a block device. It works by responding to commands like "read block 23971" and "write block 1082." A file system is a way of storing data that maps onto a block device. When you write a file, the file system code finds some free blocks on the disk, and writes your data into them. And perhaps even more importantly for this discussion, it writes other data onto the disk recording the name of the file, what blocks the file is stored in, who has access to the file, etc.
If two different machines are using the same block device, they need to coordinate their actions, or they'll clobber each other, each thinking that they get to decide where data goes on the disk and how the location of that data is recorded.
So, if you want to share a disk, the most common way to do it is to give it to one computer and have that computer own the disk, sharing it with others through a network file system like NFS or SMB. All the other computers ask for data over the network. The file server owns the disk and manages it. The clients see only files. The owner (the file server) sees files mapped onto blocks.
In a few situations, though, you want two or more computers to use a block device (a disk) directly. To do this, you need to hook those two or more computers tightly together so that they can coordinate their actions. This is called "forming a cluster." Then you need to run a cluster file system on the disk. When running Windows, without any third-party software, your only choice for a cluster file system is CSVFS. When running Linux or other OSes, you have some other options.
Again, my recommendation is to use a file server for your task. But the purpose of Shared VHDX is to allow a cluster of VMs to run a cluster file system.
This would be useful primarily (when Windows is the guest) when you want to build a SQL Server cluster out of two VMs, so that SQL itself is highly available.
Or you can build a multi-VM Windows File Server cluster using Shared VHDX. You might do this because you want your file server cluster to be available to its clients even when one of the physical hosts dies.
Without Shared VHDX, this hypothetical SQL or File Server cluster would fall off the network for a while if one of the physical hosts in your environment dies. If the hosts are themselves clustered, the VM would be restarted on another node as soon as the failure occurs. But there will be some downtime from the point of view of the clients. (With SQL Server, there will still be a little downtime, but the clients can manage that. With the File Server cluster, you can make it so that the clients, as long as they're running SMB 3.0 or later, experience automatic failover and don't drop connections.)