Whenever I talk about my relationships, I always count the two relationships I have with my kids, emphasizing that their need for me will be greater than that of any other person.
The wife and I made the decision from the start to be open to our kids, that is, not to pretend we don't see anyone else. We refer to our other partners are boyfriends and girlfriends, and they know daddy sometimes spends the night at Writer's house. While they don't see my girlfriend that often, they are in complete awe of her, and become a little manic when she is around. It's sweet that she is not simply another adult to them.
How much of of relationship you allow to develop between your son and Randy is up to you, but my own opinion is that not having Randy be a complete stranger can only be a good thing.