"Is there any pressing need to change the IP address and how do I go about doing this?"
I wouldn't have thought there was a pressing need, but it might be a prudent move, given the circumstances.
Tell your mother-in-law to pull her router's telephone line plug out of the BT wall socket before she goes to bed, and then plug it in when she gets up next morning. Her router will be assigned a new IP address, and all will be well.
As I'm sure you know, the router's IP number is not the same one that her computer has. The computer is assigned an IP number by the router itself, not by the ISP.