DATABASE CONNECTION IN ANDROID

There are 2 ways :

1) Expose the DB directly to network/internet.
2) Expose a service which read/write data from DB and call it from your apps.

In option 1), the simplest in term of architecture, you can use any DB that offer jdbc connectivity ( such mysql, oracle...) and perform request from your java code using a JDBC driver.
You need to enable the SSL flag on the client side to get a secure approach.
EX : razorsql.com/articles/mysql_ssl_jdbc.html

In option 2), the more professional, you will write code on a server (can be PHP, java web server or other) that will allow you to perform a HTTP request from your android application in order to retrieve the data through your service.
Note that you can easily secure this service using HTTPS and a basic authentication.
This solution is perfect to factorize some code related to datas for both applications.