Modify the first conf to this. Discard the second conf.
<VirtualHost *:80>
ServerAdmin webmaster@localhost
DocumentRoot /home/user/public_html/
Alias /rpm /home/user/development/rpm/public
<Directory /home/user/public_html/>
Options Indexes FollowSymLinks
AllowOverride All
Require all granted
</Directory>
<Directory /home/user/development/rpm/public/>
Options Indexes FollowSymLinks
AllowOverride All
Require all granted
</Directory>
ErrorLog ${APACHE_LOG_DIR}/rpm-error.log
CustomLog ${APACHE_LOG_DIR}/rpm-access.log combined
</VirtualHost>