I have made a form for my clients, I have made this form with a submit button at this button, the button will save the form and submit, I have made the URL go to a different e-mail address (different to mine) but when I distribute the form and it is

It doesn't matter how you've configured the submit button when you use the Distribute Form feature. It takes whatever email address is in your Identity preference (Edit > Preferences > Identity) and uses that. So you can either change the email address there or not use the Distribute Form feature and set the submit button as you want.

One thing that happens when you use the Distribute Form feature is the form is Reader-enabled, which you can do separately, but you really shouldn't do this if the form is for use by others. Each distributor of a form should Reader-enable using their licensed copy of Acrobat.