Picard has taken on proteges in the past, such as Data, Wesley, and Ro. He's always been portrayed as a teacher of sorts, and he's often taken junior officers under his wing when he felt there was potential there to be developed. I created Trys to fill a similar role to Ro's -- a character who'd shake up the status quo with her attitude, but who'd become Picard's next protege to be shaped into a better officer and person. And to be a sort of surrogate daughter to prepare Picard for his impending fatherhood.
I don't quite remember the details of T'Ryssa's role in Silent Weapons
, but my impression is that she was just minding the store at a point when things were expected to be quiet, and then circumstances forced her to stay in charge when things got serious, and she just had to bluff her way through.