Integrate a Prestashop in an existing website. (separated servers)

I would like to add an online shop (administered by prestashop) to my existing website. The shop is provided and managed by an external provider (so it cannot be on the same server than the website).

What would be a good solution to integrate the shop into my webapp?

I see 3 possibilites :

• I use the prestashop as an iframe in a page of my website (maybe there is some services or mods available to do it in a cleaner way)
• I use a custom style to make the prestashop look like it is a part of the website (however i am not very fond of making my users leave my domain)
• I use the prestashop webservices (The documentation is a bit messy, I dont even now if it is possible to add something to cart via WS)