Two WP installs on one Domain? or some other alternative for my need

I think this should be possible, but I’m having trouble searching for relevant articles in the codex. Please feel free to direct me there if you know of something that will address this.

Right now my blog is installed in the main domain, https://ponderingparenting.com. It is private so users get the login screen if they are not logged in. I would like to change it so my blog is at https://ponderingparenting.com/blog, and that is still private, but the main page, ponderingparenting.com, is a sort of welcome page, which people don’t have to login to see, but which I can post at least one post to, and which will have a link to ponderingparenting.com/blog.

If I could do this by selecting to have the front page be a static page, and somehow make that one public but everything else on the site require a login in order to view, that would be preferable. But I can’t find a plugin or understand a way to do that, and am thinking I need to have 2 instances of WordPress running–one on ponderingparenting.com and one on ponderingparenting.com/blog. If that is possible.

Please help. I have a very limited understanding of this stuff.

Thanks in advance!