TLS1.2 via SChannel: Server providing certificates instead of issuers

Question

During the TLS1.2 handshake I obtain from the server a list of trusted certificates. I assume, these should be the issuers that the server trusts. OpenSSL calles them Acceptable client certificate CA names, so these are certificate issuers!? However, the name of my client certificate is in there, but not the client certificate's issuer name. (For OpenSSL, that seems to be fine.)

Is that a mistake in the server's implementation?

Is there a way using schannel (e.g. via cURL under Windows, but also .NET) to still provide my certificate? As I understand schannel, it realizes that the issuer of my certificate is not listed there, so it does not use that certificate. Hence, the handshake fails. Can one force schannel to use a specific certificate even though the issuer is not listed?

edit 1. To clarify, I just want to talk to the server, which is not under my control. My client implementation should be based on C#/.Net and ideally schannel, thus, I'm testing up to now with cURL (schannel); the server has unfortunately to be considered as an (unknown) constant.

Thanks!