Hmm, if you don't want the hassle of a lock box, there are a couple of alternatives I can think of.
These are my suggestions, I hope something helps:
The first is to consider logical consequences if she violates your request and enters your room without asking. One could be to booby trap things. I'm not sure what other consequences would be a logical outcome for the boundary violation. A boundary needs limits or consequences or it has no impact on someone who doesn't want to respect it.
The second is a trick I use when I travel. I thought of this after I had an Airbnb host enter an apartment while I was out. A shoelace might work, but it needs to be slick if the door jamb is rough, otherwise it will stick. I use a bra strap or a tank top strap that I cut off. As I close the door jamb, I tuck in the strap two or more times, close it all the way, and take a photo. When I return, I have the photo as proof if it has been messed with, but since then, no matter where I stay, it's never been moved as it's a strong deterrent for people who are nosey (and also a warning to me that I would need someone to enter the space with me for protection if it had been messed with or removed). If your dad is in agreement, then when he enters the room while you're out, he needs to replace the string when he leaves the room and send you the new picture, otherwise he can't enter, either.
Personally, I wouldn't even tell your mom, just tell your dad and then start doing it. It will give her serious pause when she sees it, and she will not be able to put it back exactly as it was. If she overrides it, you will have proof with the photo, and you can then tell her to return what she took, and tell her if she does it again, there will be ______ logical consequence, and follow through on the consequence. Maybe your dad can help you come up with one if you can't, but enforcing it needs to come from you, not him.
The next logical step if she continues to violate the boundary even after the consequence would be to install a lock on the door without asking either of them or giving a warning, something like a hook you can put a combo lock on. Then your dad can also no longer enter when you're not there, he loses the privilege, which he should be fine with if he respects your boundary more than he wants to see the coral tank.
She can argue, rage, cajole about any of it, but I would recommend to stay firm and don't be swayed, just have a simple one-sentence statement you calmly repeat like a broken record. Hopefully your dad will back you up, but it's not necessary. They both need to respect the boundary, and be responsible for managing their own behaviors and emotions. It may be their property you're installing the lock on, but she's not respecting your property and autonomy, and you are an adult and have the right to protect yourself and your property.
