WP MU – Accessing ‘Domain-Mapped’ WP-Admin with a subdomain

Despite the fact that the plugin recommendations are off-topic here, I don’t know any other way how to do what you want to do without using a plugin.

I have experience with Domain Mapping plugin from WPMUDEV. This plugin allows you to use mapped domains for the front end and original subdomains for admin dashboard.

However this plugin is not free, but it can do what you need. Maybe there is another plugin what can do what you want, but I don’t know any.