How to make an "invisible" redirect to another domain through the path?

Question

URL Handling

There is a site#1, the content of which is displayed at the URL www.site1.ru
There is a site#2, the content of which is displayed at the URL www.site2.ru
It is necessary to display the content of the site#2 at the URL www.site1.ru/site2 without changing the host in the line browser address, that is, when visiting www.site1.ru/site2, www.site1.ru/site2 should remain in the address bar of the browser, and not change to www.site1.ru.
It is impossible to do it through mod_rewrite - www.site1.ru/site2 changes to www.site1.ru in the address bar of the browser.
Is it possible to implement this through mod_rewrite ?