Integration with another cart

For business reasons such as tax handling, payments, etc. we need to run all transactions through a third-party so they are the seller of record, but we want to use nopCommerce for everything else.  We need a third-party seller of record because our company is not equipped to manage sales taxes in all of states and countries we have a presence.  We are not a retail company, but want to sell some products on a retail market.

Here's what I want
1. User registers and logs in with nopCommerce
2. They shop and add items to the cart in nopCommerce.  I'll have some plug-ins that I'll be purchasing or creating to get the exact experience I want.
3. When they check out, I'd like to intercept this process and do the following:
   a. Get all products from the cart and add them to a cart at the third-party
   b. Display the third-party cart instead of the nopCommerce cart and allow them to perform the checkout.
   c. If the user completes the checkout, I'll empty the nopCommerce cart.

My other option is to customize the third-party offering, but it has much less out of the box functionality and I have much less control over the product than I do with nopCommerce.

I would implement it as

PaymentMethodType.Button

payment plugin. You can take a look to https://github.com/nopSolutions/paypalexpress-plugin-for-nopcommerce for sample implementation.

Thank you for the example, and that looks very much like what I want to do, except with another provider.  I do have another question - how would I remove the built-in checkout button leaving only my new button?

You could modify the cart .cshtml page and replace the button ( or change its action to redirect to your other cart)

Thank you.  That's what I ended up doing.  I don't generally like to modify the base code like that, but I don't really see any other way.