This very situation would be my BIGGEST fear about bringing a child into my home! I am so sorry you are faced with this.

Rehoming Payton sounds like the right thing to do for him, so allergy or no allergy I would say this is the right thing to do.

Now that you will have only Sammy, dealing with possible allergies should be easier. Start with air cleaners for the home. I understand they work wonders. Bathing kitty and using anti-allergen products between baths will GREATLY reduce the dander. If you cannot do the bathing, set up a schedule with a pet groomer who should be able to give you a redyce price for REGULAR appoinments. The anit-allergen products are then easy to use at home. And keep kitty out of baby's room (where he sleeps).

Most of all, best of lucky keeping kitty and keeping your son healthy.