I do not recommend to use a wildcard certificate on connection servers.
Instead you can issue one certificate for each connection server: VDI1.MyDomain.Local and VDI2.MyDomain.Local
This way the connection will be trusted when connecting from inside.
From internet you will connect to the security server only, so you only need a trusted certificate installed on the security server.
If you issue a certificate from your CA, it will work but clients connecting from internet will not trust that certificate.
If you want a certificate trusted by everyone connecting from internet, you have to buy a certificate from a certificate authority like verisign etc
In both cases, the certificate should be issued with name: view.MyDomain.com and installed on the security server only.
Hope this helps
Regards,
Claudio