Adding alias A record and A records on different domain and host

I'm a bit unsure what you mean, but let me attempt an answer:

Your server needs a certificate for the name your clients will try to reach. So for example, if you want your clients to access your service by typing https://example.com in their web browser, then your service needs to present a certificate for example.com no matter the actual FQDNs of your server(s). Then you point an A record at the IP address of your server(s) or a CNAME at their actual FQDN.

If your current DNS provider can't provide the services your company needs you should probably look at switching providers. It's entirely possible to have different companies providing your server hosting, your domain registration, and your DNS if required, if you're willing to accept the management overhead.