Long as you are using different prefixes in your database, while not advised, two different applications could run in the same database. Sounds like your hosting provider is not understanding the issue at hand, I'm afraid.
I would advise them to create a separate user for your Invision Community then if that is what they are stating here and then update your conf_global.php with those credentials.
If your hosting provider wants to separate these out and move your Invision Community to a new database, that is fine. I would not recommend doing a new installation as you would lose all data.
Are you using a plugin to manage this currently? If so, yes, the plugin would work for WordPress on our Cloud.
I'm afraid though, you would need to utilize a root domain or sub-domain on our cloud. It sounds like you have a WordPress website at your root so I would recommend something like community.example.com . If you're interested, I can move this to our Sales team who can help you in your migration to our Cloud?