You can only submit to a database if your form is bound to the database, that
is, you used the option "New from Data Connection" when you created the form,
or if you are submitting to a web service that updates a database.

Once you've bound your form to the database, you've already got one data
connection. Then you need to create a data connection to submit to the
SharePoint library, and another one to submit to an email address. Go to
Tools > Data Connections, and create those two.

Once you've got all 3 data connections set up, you can add a button to your
form and create a rule with 3 actions on it:
1. Submit using a data connection + Main data connection (= to database)
2. Submit using a data connection + SharePoint data connection
3. Submit using a data connection + Email data connection

And you're done.
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S.Y.M. Wong-A-Ton