If it is just a "normal" webspace, there would be a hosted DB-Server from your provider where you are able to use one ore more DBs on it. But you didn't have a self hosted DB-Server. Normally (and that is absolutely correct) these DB-servers are only accessible from the webspace-host. So you can't connect to that db from your xojo-desktop-app.
And you don't want to connect to a db-server through the internet, because of security reasons and so on.
What you easily could do, is to write an API. If Xojo-Apps are running on your webspace you could do that with xojo, or you could use php, perl etc.
Whese-API-Script / -Program connects to the DB and send Json or XML to your Xojo-Clients (and they are sending data to the script / programm). This way you could even use sqlite as a filebased db.
Another way is to use a "cloud db" like firebase. That has nothing to do with your webspace. It is just a way to store and read data in the cloud. I think chilkat has a xojo-plugin for firebase