Simple domain alias in address bar – is it possible?

I have two wordpress instances, each installed in a subdirectory (folder) of my main hosting site (hosted with 123-reg) and each with their own database
These are:
alexandrahunter.co.uk – actually installed in
and alexandrahunter.co.uk/main
and
alexandrahunter.co.uk/collaborationhub/
Both of these are populated – with the first having been going for a few years.

There is no wordpress installed in the public_html level, although there is a .htaccess file in there. Everything else is local to the subdirectories (folders)

I own two domain names: alexandrahunter.co.uk and liverpoolcollaborationhub.org.uk

I have (I think) pointed liverpoolcollaborationhub.org.uk at alexandrahunter.co.uk/collaborationhub – and when I type this into the browser address line, it does redirect.

However, the address line/bar/thingy shows the name of the host area (alexandrahunter.co.uk/collaborationhub/whatever) and not liverpoolcollaborationhub/whatever as I want.

Is there any way I can easily make this happen?

Thank You

And if not easily, could a kind person talk me through what I need to do to make it happen? I am not an expert.