Welcome, and thanks for your post. What you describe is essentially the same as mixed doubles, so you could adapt any mixed doubles schedule for two groups. For 12 players the format of play is critical, if you wish to play 6 rounds of simultaneous play on three courts, then there is no schedule that meets your criteria - there will be pairs of players who never oppose. It is possible to schedule it as 18 games all at different times, let me know if you want to see this.
