Advice on email not sending through Google Address

We are having an issue with sending emails from our Google account. We have a domain which sends invoices. We have been sending the emails from Google Address 1. We now need those emails to send from Google Address 2. We have changed the "from" address in all lines of code. We have also changed the username and password for our Google email account - so that it will send from Google Address 2. Everything works and sends properly from Google Address 1. However, nothing sends from Google Address 2 - once the PHP is changed to the Google Address 2 credentials. Our developers are not able to make the new address work. We do not necessarily need someone to "fix" the problem. It would be preferred that you be able to give us the "proper" steps to make this work.