Navicat works using SSH because it creates an SSH tunnel. You can do this manually from Homestead as well.
I'm assuming you're using MySQL, but let me know if you're using PostgreSQL.
From within the homestead server, run this SSH command:
ssh -L 3333:localhost:3306 username@hostname
This forwards your local port 3333 to your digitalocean server's "localhost:3306" socket, which MySQL will be listening on.
You'll need to change your username/hostname for however you connect over SSH to your DO server.
Then in your application configuration, use localhost and port 3333 to connect to the remote database.
Some more information here with explanation under Local Port Forwarding: https://serversforhackers.com/ssh-tricks/