https://www.amazon.com/dp/B01BGY6GPG
This is on sale right now for 67 bucks.
This one may be too small https://www.amazon.com/dp/B078WPCQWK
I think that having one that looks like this could be a deterrent to your MIL because it looks like business and she's not likely to be able to get into it if she tries. You won't have to worry about a key. I would just keep it out and if she asks about it, you can either say "It's to keep private things safe" or just come right out and say "It's to keep my medication safe." If she's dumb enough to ask why you need to lock up the meds, then I would definitely sit down and talk about how she has an issue, and that she's drug seeking. Tell her that you know there are better medications to try first for occasional migraines than narcotics, that actually stop the migraine vs just treating the pain. Then tell her that there are a lot of treatments for arthritis that are available to her before narcotics and she needs to see an arthritis specialist if her arthritis is so bad that she is drug seeking. I'd talk about this in front of FIL and with your husband so she is having a little intervention going on, of sorts.
I also have chronic pain and on top of that I am lucky enough to have developed severe osteoarthritis very young and I've gone through all the treatments available. We're now looking at stuff like spinal fusion so I can stop moving those bones. Her bitching about her arthritis one night is not the type of arthritis pain that needs.
Did she show signs of drug use before you moved in? Because most people don't just start raiding for pills on a whim, and especially at her age. Also, FIL seemed way too comfortable raiding your drugs for her.
I have one of those Amazon keypad security safes in my closet.
https://www.amazon.com/gp/product/B01BGY6GPG/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
I keep cash money, diaries, backup hard disks, expensive jewelry locked up inside.
I haven't ever seen one of these in person, but if the goal is cheap storage where kids can't access it, you might consider something like the Amazon Basics cabinet. If you want to double the price and add questionable fire protection, you can get something like this. As long as the goal isn't to keep out professional thieves for more than 30 seconds, you should be fine with either option.