Is it possible to point two subdomains to a private ip on a network?
For example
website1.domain.com points to 192.168.1.100 in my private network
and
website2.domain.com points to 192.168.1.101 in my private network
Both these ips would be seperate machines.
Is this possible using a service like dyndns and using their client?
Can this be done on the router connecting it to a service such as dyndns?
You should configure dynamic dns service to point to your router (e.g router.domain.com), and then configure the router to forward ports 80 and 8080 (you can choose any other 2 available ports) to your internal networks.
So, router.domain.com -> 192.168.1.100
and router.domain.com:8080 -> 192.168.1.101.