Including External Subdomain As Page Under Wix Sitemap

I have my main website stayzenden,com on Wix
I have a booking engine book.stayzenden,com hosted by rental system Lodgify

I have a link on the homepage of the Wix site named “Book Now” which links to the booking site

My problem is that the sitemap for the booking site is not included in the wix site’s sitemap. So whenever I submit the booking site url book.stayzenden,com to Google Search Console, it doesn’t recognize it as within the domain and doesn’t index it. So I made a dummy page on the wix site stayzenden,com/book that just redirects to book.stayzenden,com . However Google doesn’t like that and doesn’t score the book.stayzenden,com the same as if it were stayzenden,com/book

How should I go about adding the subdomain into the main domain’s sitemap?