Cats who urinate outside the box always have a reason, and are not doing it to be "bad". We have to try and find the reason!
First thing is a vet check for any urinary tract infection or problem,especially if this is a new behavior. Your cat may also be disturbed by the arrival of the new kitten, if you did not introduce them properly.
Some cats who are nervous or thin-skinned may pee around to comfort themselves, as this covers everything with THEIR scent - much as WE put personal belongings and pics around a hotel room to make us feel more secure.
Could she be peeing on blankets and clothes that the new kitten slept on? Is the kitten spayed/neutered?