Cannot rebind js function after removing cart item

Hi everyone. I’m facing a real issue :

I have a jQuery script transforming the cart checkout in an ajax request that send directly the client to the paiement form. The problem is when I delete an item from the cart or restore it after deleting it, it refreshs the cart and then unbind my jQuery function that makes the checkout button working as an ajax request.
I tried to add the script directly into the overrided proceed-to-checkout-button.php template on my child theme but it’s not adding it when the cart refreshs (but it’s present when I enter the cart page).
I tried to use the proceed-to-checkout action to add it but it’s not showing neither.

I’m out of solution and I don’t know why it’s not working. Please help ??