Locking cat door?

I have a prissy cat who needs her own "safe space" away from another more playful cat. His constant need for play upsets her so much she refuses to use the same litter box/boxes as him, so she ended up using the floor. He doesn't seem to understand what her hissing, growling, and swatting means. We started to use a magnetically controlled access cat door, I believe made by Cat Mate, to give her a safe space in our utility room. She wore a collar with a magnet that triggered the door to open for her. The other cat, without a magnet collar, was not allowed in that room. But he soon figured out how to push hard enough to break his way into the room. The safe room worked extremely well while it lasted. We have since moved to a new house, where I'm trying to find a better and stronger locking cat door. The only things I'm finding online that say they're strong enough to keep out animals like raccoons are made for dogs with bulky collar attachments. My girl's about 7 pounds, so she needs something fairly light, while my boy is about 15 pounds, and can break his way into whatever a raccoon can.
   
P.S. We've also tried feliway to calm her down, and we've tried putting multiple litter boxes in multiple locations.

Is your prissy female a lot smaller than the 15 lb male? And shorter? In this case, perhaps size is more important than strength of the door.
   
Perform an experiment:
   
Step 1) Measure your female's width across her face at the widest part. Add one-half inch. Measure her height to the top of her shoulderblades, behind her head. = Take a medium-sized cardboard box (that you don't need & can mutilate) that's big enough to fit the cat & a litter box. Cut a door to the measurements taken from the cat. = Cut a few 3-inch-sq. windows at the top edge of the box, for light = Place her in the box & close the box. See if she can get out. == IF SHE CAN'T GET OUT: Enlarge the hole in half-inch increments (first width, then height) until she can get out. Then proceed to Step 2. = IF SHE CAN GET OUT without squeezing too much, proceed to Step 2. (The idea is to give her the smallest possible door that she can use.)
   
Step 2) Put Large Boy inside the box & make sure he can't push the top open (tape the top shut or put a board on top of it). See if he can get out of the box. IF HE CAN'T, then he's too big to use a door that size. This may solve the problem.
   
Continuing the experiment:
   
Step 3) Put Girl Cat's next meal inside the box. Put her in front of the door, & see if she goes in to eat, then comes out again.
   
Step 4) If this works, put her litter box inside the box. Show it to her, see if she uses it.
   
IF THIS WORKS: You can build her a litter-box house & put it anywhere that works for you. It should be twice the floor space of the litter box & 18-24" high. Use 1x2's for the framework of the sides & the door; you'll need a power drill & screws, & possibly some of those steel L-brackets for the corners. Frame the door to the measurements you settled on. Use a piece of plywood for the roof. Don't put a floor on it, so you can just lift it up to get at the litter box to clean it. Use any kind of paneling you want for the walls: punched metal pieces, thin plywood, transluscent plastic panels, whatever works. Remember to have small windows (3x3 inches) if the material isn't transluscent or holey. You can paint the wood to go with your house.
   
NOTE: IF LARGE BOY CAN FIT THROUGH THE DOOR, I'll have to do some new thinking.

That idea sounds promising. I will try it and let you know how it goes. Thanks for taking the time to help!