1 WordPress for 2 domains?

Maybe this will work. Create an RSS feed with only the category or tags you want to copy over with https://www.ads-software.com/extend/plugins/wp-more-feeds/. On your domain2, create posts based on your RSS feed with https://devthought.com/wp-o-matic-the-wordpress-rss-agreggator/.

It looks like wp-more-feeds is not required. WordPress already creates feeds for categories. wp-more-feeds just makes it possible for feed discovery tools to find the feed.

The best you can do is to create a mutual subdomain for domain1.com and domain2.com so that you will have the exactly same content at either website.

Look here.

Edit: Nevermind, I misread the OP’s post.

You could probably use a plugin like feedwordpress on site2 to aggregate specific feeds from site1. You can read up on how to generate tag specific feeds in the codex.

Note this isn’t a specific endorsement of the feedwordpress plugin, I’ve only but briefly tested it. I’m sure there are plenty of similar plugins that do similar functions.

I’d also suggest reading up on duplicate content in regards to SEO.