So sorry to hear about your mum
Certainly you shpuld keep Katy in a room of her own, with attention from you and some toys, boxes to hide in, her food and water and bed and litter tray. Maybe a radio playing quietly.
Hopefully your cats will then re=emerge and start eating again.
It takes time to introduce cats and two days is wayyyyyyyyyy too short.
It could be that Katy may also be grieving and will need lots of strokes and comfort.
If you would like her to stay with you, you need to work at the introductions