I managed to redirect and keep domain_name_1.ru in the the address-bar by going to the host and creating an alias for it. Here is a list of my steps:
- created an alias for domain_name_1.ru
- created a sub domain of ru.domain_name_2.ee
- installed WP at htdocs directory
- enabled MultiSite
- created the MS network
- made the necessary MS changes to wp-config and .htaccess files in the htdocs directory
- made changes to the name servers by creating a wildcard (*) A/AAA record with redirect to the IP address
- created a new site with a domain name of domain_name_1.ru in WP MS.