What are the suitable honorifics that distinguish between a man and his father?

I know of no standard to differentiate amongst people that would have the exact same honorific. In the US, age is a typical form of distinction: "the elder Mr. Smith," "the younger Mrs. Smith," "Mr. Smith senior," or "Mr. Smith junior." A generic way would be to use their full name, e.g. Mrs. Jane Smith or Mrs. Sally Smith.

Case in point: In the film Sense and Sensibility, there is a scene involving a visit amongst Edward Ferrars, the Dashwood ladies, and an incorrect assumption. As is the apparent custom of the time, Edward acknowledges every woman according to their relative age and marriage status:

• Mrs. Dashwood (the matriarch)
• Miss Dashwood (Elinor, single, oldest sibling)
• Miss Marianne (single, middle sibling)
• Margaret (child, youngest sibling)

Elinor is in love with Edward, but guards her emotions to protect herself. The ladies believe that Edward was obligated to marry Lucy Steele. So after he greets everyone, the ladies engage in awkward but polite conversation, and ask after "Mrs. Ferrars," whom they believe to be Lucy. Edward assumes the ladies are talking about his mother, so he answers in kind. It is only when Mrs. Dashwood uses a more specific name, "Mrs. Edward Ferrars," that Edward understands the confusion. He says, "I think you mean my brother -- you mean Mrs. Robert Ferrars." After some exposition, the ladies realize that Robert married Lucy, and Edward did not. Edward is now free to marry Elinor, and more importantly, Elinor is now free to let her emotions show. The scene employs honorifics to illustrate how culture and customs can both help and hinder effective communication.

I'm not suggesting the use of antiquated cultural customs to distinguish between people with the same honorific, but specificity is generally a good thing when it comes to multiple Mr's or Ms's.