I seriously think I would consider putting an inexpensive screen door (you can get a wooden screen door for little or nothing at Lowe's or Home Depot) on your bedroom door opening with a simple latch for the inside and outside, and make that Mandy's room, complete with litter box, food and water, along with whatever else makes her happy. The others wouldn't be able to get to her, but it would be better than having to close a solid door all the time and you would still get good airflow through your house. Plus they could see each other and it wouldn't be nearly as much trouble as stacking and unstacking wooden gates every time you needed to go in and out. Sounds like she deserves some special attention right now.
I have found that the litter boxes with the raised edges on them work very well for containing the litter without having to go to a completely covered box or there are ideas for converting a tall Rubbermaid container to a litter box so that the litter doesn't get scattered all over.
Hope you can get it worked out.
