I can’t seem to recall mention of any Dornish participants in any of the mentioned tourneys in the series, am I just being forgetful or does Dorne have it’s own intra-regional tourneys? Thanks!

You’re being forgetful. Oberyn Martell is a frequent jouster, having fought in the Tourney at Storm’s End before the rebellion, and the unnamed tourney where Willas got crippled. Arthur Dayne fought at the tourney at Harrenhal, at Storm’s End, and at Lannisport in 276, etc.