Ambiguity when a sentence contains multiple possessive pronouns

There's always going to be some ambiguity, but I believe that

Billy's friend and his father were there.

is talking about the friend's father; to refer instead to Billy's father, you'd need to remove the "his":

Billy's friend and father were there.

Similarly for the other way around:

Billy's father and his friend were there.

is probably talking about the father's friend, while

Billy's father and friend were there.

is talking about Billy's friend.

To remove all ambiguity, you're gonna need to rewrite things.

Billy's friend was there, and Billy's father arrived eventually, too.

Billy's friend and his friend's father were there. The other possibility is a bit harder to rephrase concisely and unambiguously. Possibly something like: Billy's friend was there, as was Billy's father.