Windows Server 2012 r2 Hyper-v 2 External Switches

I wish I could have a setup as the following:

1. I have Windows Server 2012 R2
2. I have Two NICs: First one is connected to the LAN and the second one connected to the Internet
3. I have Created two external virtual switches: First one for the LAN NIC and the second one for the Interne NIC
4. I have create one virtual machine and promoted it to domain controller with DHCP working properly. This virtual machine has the LAN external switch.

When I create another Virtual Machine using the second external switch I got connected to the internet inside this second virtual machine.

When I add one more adapter to the second virtual machine from the LAN switch. I can not access the internet from that machine.

My question is:

How to access the internet in a virtual machine that has two adapters one from external switch to the LAN and the other with external switch to the Internet?