Having already discovered and recruited Illya Windesburg into their team, Kayden wasn't in a hurry to explore the Windesburg Hotel.
Furthermore, their situation at the Windesburg Hotel was very awkward. They had already become hostile to the Windesburg Hotel and they even doubted that if they slept in their hotel room, they might be assassinated at night.
Because of that, Windesburg Hotel was a dangerous place especially when their team was split apart. Although Illya was powerful, they still needed her to eat the Eternal Beef of Satiation so that she would be in her peak state.
In regards to Kayden's decision, Winston and Kuroneko didn't disagree with it.
Group 2 only has three members left since GoldMiner had already been sacrificed. But with Illya's addition, their group was restored to a four-member group.