Wireshark on the VM's vlan would not capture the traffic between the VM and the Thin client. You are only seeing broadcast and multicast packets.
You need to capture unicast between the virtual desktop and your thin client.
what nics are you using in the VMs? E1000 or VMXNET3?
what version of VMWare tools are installed in the instant clones ?
Please check the event logs on the virtual desktop for event ID 10400
The network interface 'vmxnet3 Ethernet Adapter has begun resetting. There will be a momentary disruption in network connectivity while the hardware resets. Event ID 10400