I can't connect when VPN is active

For starters (and this can be answered by your IT department), your VPN connection must allow for 'Split Tunneling'.  Tis a fancy way to say that it will allow some traffic to traverse one network (your home) while request to the VPN network are segmented to it specifically.  If that is not allowed, the only way to make it work is to have both PCs VPN connected.  If split tunneling is allowed, the below should help.

While different flavors of VPN can change how effective MP is, when adding a Secondary that is on your home network, and also has an active VPN, try adding the Secondary by IP instead of host name:

And then this:

Make sure you are adding the IP of the private network (your home subnet) and not that of the VPN.

Also, if your home network IPs are assigned by DHCP (and hence could change) you may want to statically assign an IP to the Secondary that is outside of the DHCP scope. For example, if you check your router config, it likely has a DHCP range;

Example:

192.168.1.2 - 192.168.1.X 

Note: your router could use 10.x.x.x but the example should still be clear

Usually the router manufacturer does not include the entire subnet but could:

192.168.1.2 - 192.168.1.254

Shorten it as it is not likely you will have 200+ devices in your home needing an address. Set it to something like:

192.168.1.2 - 192.168.1.50

Which would give you 49 DHCP addresses. After, assign your Secondary:

IP Address: 192.168.1.51
Subnet Mask: 255.255.255.0
Gateway: 192.168.1.1

Note: remember, your router may have a different subnet schema.

For clients using Cisco's AnyConnect client, and MP stops working when you use it, please see this article:

https://supportforums.cisco.com/discussion/11462471/connecting-local-lan-after-connecting-anyconnect-secure-mobility-client