New cat/old cat problems

Hello, I am new here but I felt I needed to post this since it seems to be a difficult problem.  I'll try to be brief.

My girlfriend has a 6 year old, neutered cat named Kinsey.  She as had her since she was around 3 months old and Kinsey is very close to my girlfriend.  She gets upset if my girlfriend is in the bathroom with the door closed sometimes for example.  She is a very nice and affectionate cat, just high strung.  She has lived with cats before and gotten along with them.  

This last Sunday my girlfriend and I adopted a 5ish year old male cat, also neutered, named T'challa from a shelter.  Everyone at the shelter said he loves loves loves other cats and that he is incredibly sweet, etc.  Since he got home he has mainly hidden under the bed, sometimes the closet or a box we set up.  He is eating and using the litter box and doesn't seem aggressive towards us, just not interested in coming out of hiding.  I understand that this is pretty normal, and that is fine.  The issue is that Kinsey is extremely unhappy the bedroom is closed off, especially at night.  She never slept in the bedroom with us but did sometimes spend some time in there with my girlfriend while I was getting ready to go to sleep and such.  So now she just sits outside and cries, which has caused my girlfriend to sleep on the couch as that is the only thing to get Kinsey to stop crying, and that is affecting my girlfriend's sleep and is basically just creating a stressful situation for all.  Is there any way that this can be solved?  I don't necessarily want to just open the bedroom door and let Kinsey in and then create a negative first introduction with T'challa, but I don't know what else to do.  Thank you for any help you can provide!

First, I hope you have 2 litter boxes, one for each cat.

Second, you need to get the male out of the bedroom. If you ever want to sleep again, both cats need to be out of there. Separate the two cats for now. Your female is jealous & your male is stressed in a new place. I went through this with my 3rd rescue. Best advice I read was never to let him in the bedroom at night no matter how much he cried. He stopped crying after 5 days.

We do have two litter boxes.

We could move him into an office type room we have, that would at least allow us to open up the bedroom to Kinsey so she would be less upset.  Would that upset him more though?  Any advice how he could be coaxed from under the bed, as he usually sits out of reach from all sides.  Thanks again!

He will come out eventually for the litter box, food & water. You will have to be patient as I don't know how long this will take. If he thinks you are waiting, he won't come out. He is very scared.