So.. these computers are off your network, in their space, accessing your AD? How are you establishing that? Are you doing a site-site VPN? Most importantly: why? What benefit do you both hope to realize? Since this is your AD and they are a vendor, I'd really want to see how this benefits you. Why do they want to do this with 2 AD-joined computers in their data center when there are many other ways to transfer data back and forth?
It's not unheard of, but it's unusual. Who maintains their user accounts (it sounds like you do)? Who supports the PCs? What kind of group policies do they expect to get? Why do they need access to your AD? Who maintains their access to ensure that the accounts expire when they leave the vendor company? What kind of access do they need in your network? Are you restricting their logins to only those devices? How long do they want this for?
This is a request for your legal folks as well. There needs to be a Non=Disclosure agreement as well as indemnification. Also a Business Partner Agreement that severely restricts their conduct needs to be in place.
Personally it would take an awful lot for me to agree to this. I'd really want to understand what they hope to gain from that and how they propose to implement it.