Remote access to MySQL

Good morning.

I have been searching for some information on how to remotely access MySQL and I have found many tutorials (some of them in Stackoverflow) but after having tried them all I still can not access.

The server where I have the database is a VPS to which I have full access, and the place from where I try to access this database is a hosting of a shared hosting.

These are the things I've done:

1) In the my.cnf file, I commented on the skip-external-locking line and added the line "bind-address = 0.0.0.0".

# The following options will be passed to all MariaDB clients
[client]
#password   = your_password
port        = 3306
socket      = /var/lib/mysql/mysql.sock

# Here follows entries for some specific programs

# The MariaDB server
[mysqld]
port        = 3306
socket      = /var/lib/mysql/mysql.sock
#skip-external-locking <---------------------------- ESTA LINEA
key_buffer_size = 16M
max_allowed_packet = 1M
table_open_cache = 64
sort_buffer_size = 512K
net_buffer_length = 8K
read_buffer_size = 256K
read_rnd_buffer_size = 512K
myisam_sort_buffer_size = 8M
bind-address    = 0.0.0.0 <---------------------------- ESTA LINEA

# Point the following paths to different dedicated disks
#tmpdir     = /tmp/

# Don't listen on a TCP/IP port at all. This can be a security enhancement,
# if all processes that need to connect to mysqld run on the same host.
# All interaction with mysqld must be made via Unix sockets or named pipes.
# Note that using this option without enabling named pipes on Windows
# (via the "enable-named-pipe" option) will render mysqld useless!
# 
#skip-networking

2) I have added a rule to the iptables list of the Firewall by typing the command "iptables-INPUT -i eth0 -p tcp -m tcp --dport 3306 -j ACCEPT" in the server console.

num   pkts bytes target     prot opt in     out     source               destination         
39       0     0 ACCEPT     tcp  --  eth0   *       0.0.0.0/0            0.0.0.0/0           tcp dpt:3306

3) I have entered phpMyAdmin as root and I have modified this account to change the name of the server to "%" and I have given it "ALL PRIVILEGES".

Nombre de usuario   Nombre del servidor Contraseña  Privilegios globales    Conceder
root                %                   Sí          ALL PRIVILEGES         Sí

4) Once all this is done and after restarting MySQL and Apache, I try to connect to the database using this php code and it does not do anything, it thinks:

$hostname_vps = "aqui la IP del VPS"; (también he probado con el dominio)
$username_vps = "root";
$password_vps = "aqui la contraseña para la cuenta root";
$database_vps = "aqui el nombre de la base de datos a la que quiero acceder";
$vps = mysql_pconnect($hostname_vps, $username_vps, $password_vps) or trigger_error(mysql_error(),E_USER_ERROR); 
mysql_select_db($database_vps, $vps);

This connection works if the page is hosted on the VPS so the data included here is correct. I have also tried the HeidiSQL program and the connection is successful. But if I try from the page hosted on another server nothing, there is no response.

Do I do something wrong? I do not know what else to do ...

EDITO :

In the end it turns out that the provider of the other party does not allow me to connect to a database that is not in your accommodation ...

What I've done I guess it works but with this provider I'll never know.

Thank you all for the answers, I feel the inconvenience.