After further investigation, I came to this conclusion:
1. DHCP requests through VLAN to VM Networks do not work with Realtek RTL8169 based cards.
2. Management network have no problem to get an IP address assigned on any VLAN number.
3. With Broadcom NetXtreme BCM5754, everything works as expected (se attached picture).
The reason that I wanted to swap NIC to Realtek is that MTU on my Broadcom cards is limited to 1500. If I'm trying to set anything higher than 1500 on vSwitch0, then I get an error message like "Unable to set MTU to 1501 the following uplinks refused the MTU setting:vmnic0".