provide programming solution for multiple sites using 1 DB

Job ID: 32266035

Budget: $30 – $250 USD

Project :
Challenge:
We have a mysql / php  site with a sub domain see URL in attached 
We would like to have other websites integrate our site with their site
almost like an I frame or we even replicate the site on their domain as their own subdomain with our site
The problem:
We want to have 1 database in our sites that control all other sites using their front end on different domains .

Can you assist in developing a solution like this ?
We can create an interface for all other participating sites so every user that registers from their end has a lifetime "stamp" in our one main DB almost like an affiliate that every user that they refer and register on our site or bringing other userswill carry that affiliate code .
Please tell us your solution and budget to do it 
the logo that we have should stay
it just need to integrate with other websites in a smart way that user can register on another site and do all activities like on our site but the database is on our end 
We are sure this can be done., but not sure how
we will proceed with your solution if your solution make sense 
environment is LAMP
Thanks
This project is just to provide a tech solution and then your estimate to do this for us 
Related categories: PHP Engineering Software Architecture MySQL Web Hosting