According to your information, do you have different mail domain (contoso.com) with AD domain (netware.com)?
If so, I suppose you may need one certificate for contoso.com including at least these two urls:
autodiscover.contoso.com
Webmail.contoso.com
And since you are having a parent-child domain structure, you may also need to include the child domain urls in the certificate for users to connect to the Exchange servers in child domain:
autodiscover.child.contoso.com
Webmail.child.contoso.com
About virtual directorie urls, it is usually recommended to set the internal urls to be the same as external ones.
In your case, it should be set to Webmail.contoso.com and Webmail.child.contoso.com.
Otherwise, internal clients would throw certificate warnings when they connect to Exchange servers, as the url groundfloor.netware.com isn't included in the certificate.
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