We have 2 cats and my husband and I are allergic and we all live in harmony! It's a lot of extra work, but it's worth it if you love your cats.
1. You're doing good by keeping the cats out of the bedroom. Get her a good air cleaner with a HEPA filter and run it constantly. We use the Honeywell ones. It would be a good idea to do a deep cleaning of her bedroom, get the carpets shampooed, etc. Don't forget to wipe down her walls! I would get rid of as much carpet as possible since cat dander sticks to the carpet.
2. Invest in a laundry detergent that removes allergens. It can be expensive so I just use that detergent to clean sheets.
3. Wipe down the whole house. Get all your carpets shampooed if you can. Wipe down the walls and furniture. Dander sticks to walls and the ceiling too.
4. Take down any drapes and wash them in allergen detergent.
5. Get a solution called "Allerpet." You put it directly on the cat and it neutralizes the dander. You can buy it online. I apply it by putting it on one of those sponges with the sticks that are used for painting. Then you can go against the way their hair grows and get the Allerpet on the cat's skin without using a lot of it. I alternate every day between applying Allerpet and wiping the cat down with wipes that also neutralize dander.
6. They make a spray that also neutralizes dander that you can spray on your furniture. All of this can be purchased online at a store that specializes in allergy solutions.
7. Vacuum every day or every other day with a vacuum with a HEPA filter.
8. I invested in a steam cleaner. The steam neutralizes dander as well, so I steam our floors and furniture twice a week. It doesn't take long, and it's better and cheaper than using the sprays. I spray the furniture down with the allergen spray every 2 weeks.
9. We have an air filter in the living room where the cats are likely to be.
10. We covered the cat box with 2 covers. Cat urine and feces can have dander so cleaning the box 1-2 times a day helped. We also switched litter to a dust-free wheat litter.
11. Make sure your daughter drinks lots of water. Drinking water helps tame the histamine reaction.
12. We don't use over-the-counter meds, we use natural Bromelain and Quercetin supplement and vitamin C.
13. Your daughter should wash her hands whenever she touches the cat.
14. If you can bathe your cat, it helps. Some cats won't tolerate it. Mine will so I bathe them once every 2 weeks in a natural shampoo that gets rid of allergens.
We do all of these things to the best of our ability. I used to be very allergic to cats and now I'm only affected if I pet them and then touch my eyes. My husband's asthma has lessened considerably--enough so we can keep the cats and it is managed with an inhaler (which he is supposed to use anyway). The strategy is 2-fold, get rid of the allergens in the house and lessen the allergens produced on the cats.
My brother is very allergic to cats and he can come over and has no issues. Most people who come over don't have issues with our cats.
Good luck! I would try all of these things before you get rid of the cats. I know my one cat is very attached to me and if I gave her up she would cry so much and be so sad that she'd have to be put to sleep. She cried nonstop for 2 weeks when I left her with my ex-husband, so he told me to come get her. It would be a death-sentence for her to go to a shelter.
If you have questions, message me and I'll be happy to help! Good luck!