When introducing a new cat to a home, it is best to do it very slowly. I introduced a new kitten to my home which already has a 2 year old cat. As strongly recommended by the vet, we kept the kitten behind closed doors unable to see the other cat for a week. They became curious and eventually began playing together with their paws under the door. Then the next week we would switch them for about an hour allowing the new kitten to walk around the house without fear of the other. The next week they would play together, supervised, for a few hours a day when we were home from work. After about 3 weeks we were able to leave them alone together, and now they are best friends. They cuddle, play, etc.
It is a very long process, but in the best interest of you and your cats, that is the way to go.
More than likely, it is your oldest cat that is peeing, since she feels as if her home is being taken over by another cat. I would pay extra attention to her, give lots of love, play with her, etc. Unless she has an infection, she is only trying to communicate to you.