Migrating server

[rferbesa]

I have a Server#1 with this configuration for the Let's encrypt certificate:
VIRTUAL_HOST=mysubdomain1.mydomain.com
LETSENCRYPT_HOST=mysubdomain1.mydomain.com

Now I have a newer Server#2 (more resources, more features...) with this configuration for the Let's encrypt certificate:
VIRTUAL_HOST=mysubdomain2.mydomain.com
LETSENCRYPT_HOST=mysubdomain2.mydomain.com

My iOS/Android apps work well in both cases (pointing to mysubdomain1.mydomain.com and to mysubdomain2.mydomain.com).

At some moment I would like to migrate from Server#1 to Server#2 but I don't have too much experience with docker and I'm a bit confused on how to do it with the least risk.

If I configure Server#2 to this:
VIRTUAL_HOST=mysubdomain1.mydomain.com
LETSENCRYPT_HOST=mysubdomain1.mydomain.com
or even
VIRTUAL_HOST=mysubdomain2.mydomain.com,mysubdomain1.mydomain.com
LETSENCRYPT_HOST=mysubdomain2.mydomain.com,mysubdomain1.mydomain.com

I guess this will not work because Let's encrypt will not access Server#2 through mysubdomain1.mydomain.com (this subdomain would keep pointing to Server#1) so the certificate will not be installed in Server#2.

Then should I do something like this?:
-turn off Server#1
-change mysubdomain1.mydomain.com DNS so it points to Server#2.
-change Server#2 configuration to
VIRTUAL_HOST=mysubdomain1.mydomain.com
LETSENCRYPT_HOST=mysubdomain1.mydomain.com
-restart docker and trust that Let's encrypt certificates are generated correctly for Server#2.

Is there any better solution for this migration?