"I know that you two meet frequently."
Translation:So che voi due vi incontrate frequentemente.
You need the vi here because it's the reflexive pronoun. Vi incontrate means you meet each other.
Vi is neither the article nor the subject pronoun (which you can eliminate), and because it's part of the reflexive verb you have to use it as a direct object pronoun..
Since knowing is something certain rather than something doubtful or questionable, I think the indicative is appropriate.