Elphaba is being a bully. She picks on the kid because she wants to assert dominance or status over said kid. It is probably made worse because the kid is afraid of Elphaba and Elphaba is working this perceived weakness.
It is especially not ok that Elphaba is putting her mouth on people in any way. When the kid comes over, Elphaba should always be on a leash. Don't just put her away because this avoids fixing the issue. If Elphaba attempts to jump or nip, give her a VERY FIRM COLLAR POP and a stern verbal correction. If this were my dog, I would grab her muzzle, look her in the eye and make it clear that the Righteous Retribution of the heavens would rain down on her if this behavior was seen again. It is not her job to bully guest in your home even if you hate your crumby little cousin.
That, however, is just the consequence for bad behavior. You need to start working on some foundation obedience NOW so that Elphaba can have a GOOD job to do when guests come over. Teach a sit. Then teach a sit/stay. Then a sit/stay/exam.
A good sit stay is accomplish on leash. Never off leash!!!!!! Sit the dog. Put your hand in front of the dog's face and moving your hand towards the dog's face say in a clear voice "STAY". Step away from the dog 2 steps only (going too far too soon is too much for a young dog). If she tries to follow you or she breaks, don't say anything. Just take her by the collar and push her back into place. YOU DON'T EVER WANT TO REPEAT A COMMAND OR A DOG WILL EXPECT TO BE TOLD 5 TIMES TO DO SOMETHING BEFORE IT EVER COMPLIES. If Elphaba is holding her sit, count to 10 and then say OK! Break her off. Party Party Party. Treat. Let her know she has done a great job!!!!!
Then repeat the exercise. Do it no more than 3 times and then be done. Do this exercise 3X a day. Work up to being able to stand at the end of a 6-8 foot leash for a full 3 minutes without Elphaba moving or lying down. If you have been working the exercise and she continually breaks, you might go to giving her a firm collar pop under the chin so that she knows that STAY is something she has to do. This exercises should also be worked with the DOWN command.
Next. You know sit/stay. Now progress to SIT FOR EXAM. With this, the dog is told to SIT/STAY but then a person comes over and pets the dog on the head and back. Start easy. Have someone come and touch Elphaba's head and then walk away. Ok! Break her off Party!!!! If Elphaba breaks or gets up. Put her back into her sit. DON'T SAY ANYTHING!!! Work up to being able to have someone touch Elphaba all over without her moving.
So then when the evil cousin comes over. Put Elphaba in a sit/stay. Encourage cousin to pet Elphaba's head. Everyone is happy. (Still keep her on a leash to manage behaviors!)