Roy's intention was clear, the more clashes there were in the city, the more people would get involved and the more cards would he be able to discover.
He was trying to have his opponents fight and tire out each other, before he actually entered the ring and either killed or defeated the rest of them.
Lady Kate stood to gain from this as well, as it was clear that the dominions officials and nobles were trying to keep a wait and see approach. They would chose a side only if forced to.
In the meantime she could gather a few favors left and right, as she increased the following behind her son's faction.
Even then, she couldn't help but feel that she was actually fighting a losing battle knowing that Roy would most probably not allow her son to become the lord of the dominion.
She knew her son perfectly, and he was the type to get easily agitated, and frustrated, as he wouldn't even be able to control his emotions and consider the big picture.