I need to integrate "The Booking Button" with websites I create for Hotels & Lodges

Ok so...

Firstly, The Booking Button is not a button you add called "booking". It is a standalone software integration accessing mainframes and is used similar to how uou book on booking.com etc, to help people book specific rooms, their preferences etc. And pay. 

I have to pitch at 10am CAT today, to a big hospitality software company, and they want the button added to features, including Mailchimp newsletters etc. If you can't use this specific product, PLEASE recommend an alternative. PayPal will be used, as well as PayFast which is a bonus. They currently did their newsletters on Canva....then sent them ads PDF attachments...not ideal...

I'm not sure if I understood your question correctly. Do you want to embed a form you created to your website? If so please check the following guide:

Which Form Embed Code Should I Use

If you want to achieve something else, please provide us more details.

To integrate a form with Mailchimp, please check this guide:

How to Integrate with MailChimp

Also, please note that multiple payment fields cannot be added to a form. However, there is a workaround to create a multiple payment form.

How to Create a Basic Multiple Payment Form