Could you attach a screenshot of your vSwitches so I can see the configuration?
as per output your vmnic1 is down. ideally you should have one route for management network, then the traffic will be handled from same nics only..
ESXi (management) interfaces are not physical NICs (vmnicX). They are virtual vmkernel interfaces (vmkX) bound to vSwitches which in turn have physical uplinks assigned.
If you want vmkernel traffic to be forwarded through specific physical NICs, you have to configure your vSwitches and vmkernel ports appropriately.
Post the output of the following shell commands to get a full picture:
esxcli network vswitch standard list
esxcli network vswitch dvs vmware list
esxcli network ip interface list
esxcli network ip route ipv4 list
esxcli network ip interface ipv4 get