Fix mailing issues on 2 websites

1. I have a CakePHP website, running on Godaddy hosting. The problem is that mails sent by the website, often don't arrive in the users mailbox. (Specifically: the 'forgot password' email often doesn't arrive.) The website is an image gallery, running on 9 domains using 9 languages. I heard Godaddy can be hard (strict) for sending emails, so someone who has experience with the Godaddy mailing system would be a plus. At Godaddy, I have access to Cpanel. I'm open to using an smtp service, if needed. 2 CakePHP developers already took a look at this, and were not able to solve it, so I would like someone who is specialised infixing mailing issues. 2. On the same server, I have a Wordpress site. The emails from that website don't arrive either. There is a Woocommerce webshop there, but when an order is placed, the mails don't arrive.