Cross Domain form submit Google Tag Manager auto trigger

I have some problem while getting data from another site. In this case I want to get the reservation data from the booking engine site and they want to pass the data to me with Google Tag Manager. I don't really understand what I should do when they just need GTM code. What I should create in my server to get the data from the booking engine with Google Tag Manager ?

This is the illustrations:

I have two sites called sites1.com and sites2.com. In sites1.com I put the Google Tag Manager scripts to push form submit data like full name, last name, email, etc. After somebody submit the form I want to get the submited data in sites1.com to sites2.com with Google Tag Manager. My problem is how to get the data after somebody submited the form in sites1.com in my sites2.com ?

Please anybody knows how to resolve my problem . Thanks in advance .

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